UNIVERSITY  OF  CALIFORNIA 
AT   LOS  ANGELES 


GIFT  OF 

<RNEGIE  INSTITUTE: 
OF  WASHINGTON 


A  BICYCLE  ERGOMETER 

WITH  AN 

ELECTRIC  BRAKE 


BY 
FRANCIS  G.  BENEDICT  AND  WALTER  G.  CADY 


WASHINGTON,  D.  C. 

PUBLISHED  BY  THE  CARNEGIE  INSTITUTION  OF  WASHINGTON 
1912 


A  BICYCLE  ERGOMETER 

WITH  AN 

ELECTRIC  BRAKE 


BY 

FRANCIS  G.  BENEDICT  AND  WALTER  G.  CADY 


WASHINGTON,  D.  C. 

PUBLISHED  BY  THE  CARNEGIE  INSTITUTION  OF  WASHINGTON 
1912 


CARNEGIE  INSTITUTION  OF  WASHINGTON 
PUBLICATION  NO.  167 


ISAAC  H.  BLANCHARD  COMPANY 
NEW  YORK 


op 


CONTENTS. 


PART  I. 

Page 

Introduction 3 

Detailed  description  of  the  bicycle  ergometer 5 

General  considerations  regarding  method  of  use 7 

Method  of  calibration 9 

PART  II. 

Calibration  tests 11 

The  technique  of  a  calibration  experiment 12 

Calibration  tests  of  Ergometer  I 14 

Earlier  calibration  tests 14 

Calibration  tests  of  1911 15 

Friction  tests  with  Ergometer  I 21 

Calibration  tests  of  Ergometer  II 22 

Friction  tests  with  Ergometer  II 29 

PART  III. 

The  magnetic  reactions  produced  by  a  copper  disk  rotating  between  the  poles 

of  a  magnet 31 

Measurement  of  magnetic  field  by  means  of  a  bismuth  spiral 33 

Comparison  of  results  with  theory •. .  . .  37 

Further  experiments  with  the  eddy  currents 39 

Influence  of  temperature  on  the  constancy  of  the  bicycle  ergometer 42 

The  design  of  electric  brakes 42 


ILLUSTRATIONS. 

Page 
FIG.  1.  Side  and  top  views  of  Ergometer  II 5 

2.  Electro-magnet  and  copper  disk  of  Ergometer  II 6 

3.  Scheme  for  calibration  of  the  ergometer  in  a  respiration  chamber 13 

4.  Heat  per  revolution  of  Ergometer  I  for  currents  of  0.7  and  0.8  ampere 

through  the  field 18 

5.  Calibration  curve  of  Ergometer  I  for  magnetizing  current  of  0.9  ampere.         19 

6.  Calibration  curve  of  Ergometer  I  for  magnetizing  current  of  1.1  am- 

peres           19 

7.  Calibration  curve  of  Ergometer  I  for  magnetizing  current  of   1.25 

amperes 20 

8.  Calibration  curves  of  Ergometer  I  for  magnetizing  current  of  0.7  to  1.25 

amperes 21 

9.  Calibration  curve  of  Ergometer  II  for  magnetizing  current  of  0.95 

ampere   24 

10.  Calibration  curve  of  Ergometer  II  for  magnetizing  current  of  1.10 

amperes 24 

11.  Calibration  curve  of  Ergometer  II  for  magnetizing  current  of  1.35 

amperes 25 

12.  Calibration  curve  of  Ergometer  II  for  magnetizing  current  of  1.50 

amperes 26 

13.  Calibration  curves  of  Ergometer  II  for  magnetizing  current  of  1.25 

amperes 27 

14.  Calibration  curves  of  Ergometer  II  for  magnetizing  current  of  0.95  to 

1.50  amperes 28 

15.  Magnetic  induction  across  the  air-gap 35 

16.  Magnetic  lines  and  current  loops  on  surface  of  rotating  disk 40 


209177 


A  BICYCLE  ERGOMETER  WITH  AN 
ELECTRIC  BRAKE 


PART  I. 


INTRODUCTION. 

A  practical  application  of  thermodynamic  principles  that  has  inter- 
ested economists  and  physiologists  has  been  the  problem  of  determining 
the  mechanical  efficiency  of  the  human  body  as  a  machine.  Not  only 
were  the  earlier  writers  handicapped  by  an  inability  to  determine  accu- 
rately the  intake  of  energy  by  the  body  in  food  and  drink — a  handicap 
that  has  since  been  admirably  overcome  by  the  use  of  the  accurate  calori- 
metric  bomb — but  they  were  likewise  handicapped  by  an  inadequate 
measurement  of  the  mechanical  output  of  the  individual  experimented 
upon.  A  study  of  this  subject,  therefore,  must  divide  itself  into  two 
parts:  first,  the  determination  of  the  intake  of  energy,  and  second,  the 
measurement  and  computation  of  the  amount  of  work  done.  The  present 
paper  is  concerned  with  the  second  of  these  two  divisions. 

Without  going  into  an  extended  historical  discussion  relative  to  this 
subject,  it  may  be  said  that  the  attempts  to  make  computations  of  the 
intake  and  output  of  energy  have  been  very  numerous  and  for  the  most 
part  extremely  crude,  those  of  the  output  of  energy  dealing  usually  with 
the  work  of  either  the  arms  or  the  legs.  Among  the  various  methods  used 
for  studying  the  amount  of  work  done  by  the  arm  may  be  mentioned  the 
lifting  of  weights,  the  filing  of  cast  iron,  pulling  up  weights  by  means  of  a 
rope,  shoveling  earth  to  a  height  of  about  2  meters,  pulling  on  an  oar, 
pumping  water,  hammering,  turning  a  crank  or  winch,  and  the  more  ac- 
curate method  recently  employed  by  Zuntz1  of  using  a  brake  ergometer, 
and  Johansson2  of  raising  weights.  In  tests  with  the  leg-motion,  the  mus- 
cular work  has  been  for  the  most  part  confined  to  lifting  the  body  to  a 
definite  height  by  ascending  a  ladder  or  stairs,  carrying  weights  up  stairs, 
wheeling  a  loaded  wheelbarrow  up  an  incline,  walking  on  a  treadmill,  and, 
more  especially,  riding  a  bicycle  or  an  apparatus  similar  in  form. 

In  studying  the  muscular  work  in  the  leg-motion  of  bicycling,  a  special 
apparatus  has  been  extensively  employed.  One  of  the  earlier  types  of 
this  machine  was  that  described  by  Atwater  and  Benedict,3  in  which  a 
pulley  attached  to  the  armature  shaft  of  a  small  dynamo  was  pressed 
against  the  rear  wheel  of  a  bicycle;  the  current  generated  by  this  dynamo 
as  it  revolved  by  the  movement  of  the  pedals  was  then  measured.  By 
using  the  dynamo  as  a  motor,  the  machine  could  also  be  calibrated. 

1  Zuntz,  Archiv  fur  (Anat.  und)  Physiol.,  1899,  Suppl.,  p.  39. 

2  Johansson,  Skand.  Archiv  fur  Physiologic,  1901,  11,  p.  273. 

3  Atwater  and  Benedict,  U.S.  Dept.  Agr.,  Office  Expt.  Stas.  Bui.  136, 1899,  p.  30. 

3 


4  A  BICYCLE   ERGOMETER  WITH  AN  ELECTRIC    BRAKE 

Recently  a  brake  ergometer  employing  bicycle  pedals  has  been  used 
with  considerable  success  by  Amar,1  while  in  a  private  communication 
Dr.  Krogh  writes  of  a  bicycle  ergometer  which  he  is  using  in  collaboration 
with  Dr.  Lindhard,  in  which  the  principle  of  the  electric  brake  plays  an 
important  role. 

Numerous  tests  have  also  been  made  to  compute  the  energy  trans- 
formations of  a  bicyclist  while  traveling  on  the  track  against  the  resistance 
of  air,  wheels,  tires,  and  chain.  This  was  considered  by  Prof.  R.  C.  Car- 
penter2 in  connection  with  the  amount  of  energy  consumed  in  a  bicycle 
race,  but  was  much  more  satisfactorily  determined  by  Berg,  duBois 
Reymond,  and  Zuntz3  by  means  of  a  bicycle  towed  around  the  track  by 
a  motor  cycle.  In  every  instance  thus  far  cited,  it  was  necessary  to  con- 
vert the  foot-pounds  or  kilogrammeters  into  calories,  the  accuracy  in  the 
measurement  of  foot-pounds  or  kilogrammeters  being  the  criterion  of  the 
apparatus.  In  practically  all  instances,  owing  to  the  difficulty  of  determ- 
ining these  mechanical  quantities  exactly,  the  apparatus  was  by  no  means 
so  accurate  as  the  best  physiological  experimenting  can  to-day  demand. 

Certain  muscular  exercises,  such  as  swimming  or  rowing  with  sliding 
seats,  unquestionably  bring  into  play  more  muscles  than  does  the  exercise 
of  bicycle  riding;  on  the  other  hand,  the  stationary  position  of  the  body, 
particularly  of  the  head,  makes  the  exercise  of  riding  on  a  stationary  bi- 
cycle distinctly  advantageous  for  a  study  of  the  respiratory  exchange, 
especially  when  the  subject  has  to  breathe  through  a  mouthpiece  or  nose- 
piece,  or  through  some  other  form  of  breathing  appliance.  Furthermore, 
as  has  been  frequently  demonstrated,  most  intense  muscular  exercise  can 
be  produced  by  means  of  the  powerful  leg  muscles;  hence,  in  any  study  of 
metabolism  during  muscular  work,  all  of  these  advantages  seem  to  point 
toward  the  desirability  of  utilizing  some  form  of  bicycle  motion  for  the 
muscular  work. 

The  great  difficulty  with  the  earlier  types  of  bicycle  ergometers,  how- 
ever, has  been  the  uncertainty  of  the  amount  of  work  performed,  for  even 
with  the  apparatus  of  Atwater  and  Benedict  there  was  considerable  slip 
of  the  contact,  and  the  determination  of  the  work  done  was  by  no  means 
satisfactory.  With  other  forms  of  ergometers,  in  which  there  is  the  fric- 
tion of  a  band,  or  belt,  or  weight,  the  uncertainty  and  variations  in  the 
resistance  must  always  be  reckoned  with. 

Mr.  0.  S.  Blakeslee,  formerly  mechanician  of  Wesleyan  University, 
made  the  ingenious  suggestion  that  an  electric  brake  be  used  for  applying 
a  constant  source  of  resistance  in  a  bicycle  ergometer.  This  later  form 
of  apparatus  consisted  essentially  of  a  bicycle,  the  rear  wheel  of  which  was 
replaced  by  a  copper  disk  which  rotated  between  the  pole-faces  of  an 
electro-magnet.  The  usual  form  of  pedal,  sprocket-wheel,  and  sprocket- 

1  Amar,  La  Rendement  de  la  Machine  humaine,  Paris,  1910. 

»  Atwater,  Sherman,  and  Carpenter,U.S.Dept.Agr.,  Office  Exp.Stas.Bul.98, 1901,  p.57. 

1  Berg,  duBois  Reymond  and  Zuntz,  Arch,  f .  Anat.  u.  Physiol.,  Physiol.  Abt.  1904,  p.  20. 


INTRODUCTION  5 

chain  was  used  to  convey  the  power  from  the  foot  to  the  disk.  The  first 
form  of  this  instrument  has  been  described  in  detail  in  a  former  publica- 
tion by  Benedict  and  Carpenter.1  A  second  apparatus  was  constructed 
during  the  summer  of  1911  by  Mr.  W.  E.  Collins,  mechanician  of  the 
Nutrition  Laboratory,  and  carefully  tested.  The  original  ergometer 
leaves  little  to  be  desired  in  the  way  of  accuracy,  constancy,  and  sub- 
stantial construction,  but  as  certain  modifications  have  been  made  in 
constructing  the  second  instrument,  a  detailed  description  of  this  ergom- 
eter seems  desirable. 

DETAILED  DESCRIPTION  OF  THE  BICYCLE  ERGOMETER. 
For  the  latest  form  of  bicycle  ergometer,  which  is  shown  in  fig.  1,  a 
high-grade  bicycle  frame,  with  sprockets  and  pedals,  was  purchased. 
Instead  of  the  ordinary  sprocket-chain,  a  special  chain  was  used  in  which 


FIG.  1. — Side  and  top  views  of  ergometer  II. 


the  minimum  resistance  and  maximum  flexibility  were  secured  by  roller 
bearings  in  the  links.    The  rear  wheel  was  replaced  by  a  hub  of  the  type 

1  Benedict  and  Carpenter,  U.  S.  Dept.  Agr.,  Office  Expt.  Stas.  Bui.  208,  1909,  p.  11. 


6 


A    BICYCLE    ERGOMETER   WITH    AN   ELECTRIC    BRAKE 


commonly  used  on  motor  cycles,  which  was  fitted  to  a  large  copper  disk, 
40.5  cm.  in  diameter  and  approximately  6  mm.  thick.  A  wooden  split 
pulley  (W,  fig.  2)  was  also  placed  upon  the  hub  for  experiments  in  which 
the  apparatus  would  be  driven  by  an  electric  motor.  This  has  been  of 
especial  value  in  some  physiological  tests  on  coasting  in  which  the  ergom- 
eter  was  driven  by  a  motor,  the  feet  of  the  man  being  on  the  pedals  and 
revolving  without  doing  any  work. 

The  apparatus  was  substantially 
mounted  upon  a  base-board  by  means 
of  iron  braces.  A  type  of  handle-bar 
was  selected  which  could  be  comfort- 
ably adjusted  for  the  various  riders 
who  were  to  use  the  ergometer,  and 
the  seat  was  also  adjustable  to  any  de- 
sired position.  Provision  was  likewise 
made  for  recording  the  revolutions  of 
the  pedals  by  means  of  a  mechanical 
counter  attached  near  the  pedal- wheel 
hub  so  as  to  be  actuated  by  each  pedal 
revolution. 

The  electro-magnet  used  for  the 
brake  was  made  of  a  high-grade  mag- 
net iron,  which  subsequent  tests 
showed  to  be  especially  satisfactory. 
The  general  construction  and  the 
method  of  mounting  are  shown  in  fig. 
2.  The  length  of  the  magnet,  exclu- 
sive of  the  yoke,  was  14.7  cm.,  and  the 
dimensions  of  the  pole-faces  P  P'  were 
as  follows:  length,  6.4  cm.;  width,  5.1 
cm.;  thickness,  2.8  cm.  The  magnet 
was  wound  with  double  cotton-covered 
magnet  wire,  substantially  mounted 
on  a  framework  made  of  standard  %- 
inch  brass  piping,  and  attached  to 
the  iron  braces  supporting  the  bicycle. 
Four  binding-posts  at  the  top  of  the 
magnet  provide  for  joining  together 

the  two  magnet  coils  C  C'  and  likewise  permit  the  connection  with  the 
electric  current  used  to  magnetize  the  field  and  with  the  mil-ammeter 
which  measures  the  current.  When  mounted  on  the  brass  support,  the 
magnet  was  so  adjusted  that  the  disk  D  rotates  in  the  gap  between  the 
pole-faces  P  P'  with  approximately  1  mm.  air-space  on  each  side.  The 
upper  edge  of  the  pole-faces  forms  a  line  which  is  tangential  to  the  cir- 
cumference of  the  copper  disk. 


FIG.  2. — Electro-magnet  and  copper  disk  of  er- 
gometer II.  The  copper  disk  D  rotates  in  a 
magnetic  field  between  pole-faces  P  and  P'. 
Currents  of  varying  strength  are  passed 
through  coils  C  and  C',  thus  varying  the  in- 
tensity of  the  magnetic  field.  The  grooved 
wooden  pulley  W  is  used  to  drive  the  machine 
by  a  belt  from  a  motor. 


INTRODUCTION  7 

In  constructing  the  magnet  we  were  at  a  disadvantage  in  not  knowing 
the  exact  dimensions  of  the  magnet  in  the  first  ergometer,  and  since  no 
records  were  available  as  to  the  size  of  the  wire,  we  were  obliged  to  make 
an  approximate  estimate.  It  was  found  subsequently  that  in  order  to 
secure  a  sufficiently  strong  magnetic  field  with  a  moderate  current,  it  was 
necessary  to  rewind  the  magnet  with  a  smaller  size  of  wire  (No.  19  B.  &  S. 
gauge),  0.91  mm.  diameter,  thus  increasing  the  total  resistance  to  10  ohms. 

With  this  winding  of  the  magnet  it  was  found  that  a  current  of  1.5 
amperes  through  the  coil  produced  substantially  the  same  drag  effect  as 
did  1.25  amperes  on  the  older  machine.  The  new  machine  has  a  dis- 
advantage in  that  it  develops  a  larger  amount  of  heat  in  the  magnet  coil 
itself  than  the  first  ergometer,  thus  making  a  somewhat  larger  correction 
to  be  deducted  from  the  total  heat  measured  if  the  apparatus  is  used 
inside  a  calorimeter.  As  a  matter  of  fact,  with  a  current  of  1.5  amperes 
through  the  field,  the  heat  development  in  the  magnet  itself  is  17.8  to  17.9 
calories  per  hour,  while  with  the  older  form  of  apparatus  with  a  current 
of  1.25  amperes  through  the  field,  the  heat  development  was  10.9  calories 
per  hour. 

GENERAL  CONSIDERATIONS  REGARDING  METHOD  OF  USE. 

When  the  ergometer  is  in  use,  a  variable  resistance,  which  consists 
of  German-silver  or  manganin  wire,  is  placed  in  series  with  the  magnet  coil 
and  the  mil-ammeter.  By  altering  the  variable  resistance,  the  current 
is  kept  constant  throughout  any  experiment.  At  the  beginning  of  an 
experiment  the  coil  is  cold,  and  if  the  adjustable  resistance  is  set  at  a 
given  point  the  current  passing  through  the  magnet  gradually  decreases 
as  the  field  begins  to  warm  up;  it  accordingly  becomes  necessary  to  ad- 
just the  resistance  until  the  desired  amount  of  current  through  the  field 
is  obtained.  In  approximately  20  minutes  to  half  an  hour  constant 
temperature  conditions  are  obtained  and  thereafter  no  material  adjust- 
ment of  the  resistance  is  necessary.  The  larger  sprocket  has  26  teeth 
and  the  smaller  sprocket  8,  the  ratio  being  1  to  3.25.  While  one  can  com- 
pute from  the  number  of  revolutions  the  distance  that  theoretically 
would  have  been  traversed  had  the  subject  been  riding  a  bicycle  with  a 
standard  wheel  of  28  inches,  this  really  has  very  little  significance,  as  of 
course  in  riding  a  stationary  bicycle  there  is  no  wind  resistance  and  there 
is  no  energy  expended  on  tires;  consequently  it  is  necessary  to  supply 
sufficient  resistance  to  the  copper  disk  to  compensate  for  the  absence  of 
these  factors. 

With  this  ergometer  it  was  possible  within  certain  limits  to  vary  the 
amount  of  work  done  per  hour  by  varying  the  speed  of  revolution  of  the 
disk.  But  few  riders  care  to  ride  for  any  length  of  time  at  less  than  50 
revolutions  of  the  pedal  per  minute,  and  tests  on  a  number  of  individuals 
have  shown  that  the  revolutions  usually  ranged  from  55  to  80  per  minute; 
with  highly  trained  professional  bicyclists,  the  rate  of  revolution  may  rise 


8  A   BICYCLE    ERGOMETER   WITH   AN    ELECTRIC    BRAKE 

as  high  as  100  to  120,  or  indeed,  for  short  periods,  to  135  or  140.  To  in- 
crease the  amount  of  work  done  it  is  necessary  to  alter  not  only  the  speed, 
but  more  particularly  the  magnetic  drag  upon  the  disk.  This  is  done 
by  increasing  the  current  through  the  field.  The  lowest  current  that  has 
been  used  with  the  new  instrument,  either  in  actual  riding  or  in  the  cali- 
bration of  the  ergometer,  has  been  0.95  ampere,  and  the  highest  1.5  am- 
peres. With  the  earlier  form  of  instrument,  the  current  varied  from  0.70 
to  1.25  amperes. 

Certain  fundamental  criticisms  can  be  made  as  to  the  propriety  of 
comparing  the  metabolism  of  a  subject  riding  on  a  stationary  bicycle 
with  that  of  a  man  riding  a  bicycle  in  the  open  air  or  on  the  track.  Under 
the  latter  condition  there  is  a  very  rapid  movement  of  air  against  the 
body  of  the  subject,  with  increased  respiration,  and  hence  a  temperature 
regulation  due  to  the  vaporization  of  water  from  the  skin.  There  is  also 
a  certain  stimulus  due  to  the  presence  of  spectators.  The  psychical 
conditions  are  unquestionably  markedly  different  in  ordinary  bicycle 
riding  from  those  obtained  when  riding  a  stationary  bicycle  in  the  confines 
of  a  laboratory,  and  especially  in  the  confines  of  a  respiration  chamber. 
That  this  psychical  stimulation  unquestionably  plays  an  important  role 
in  securing  the  greatest  output  of  heat  and  mechanical  work,  particularly 
in  momentary  special  exertion  incidental  to  a  spurt,  no  one  can  deny. 
On  the  other  hand,  experimental  evidence  thus  far  accumulated  seems  to 
indicate  that  the  relations  between  the  total  energy  output  of  the  body 
and  that  actually  transformed  into  heat  by  the  ergometer  remain  for 
the  most  part  essentially  unaltered;  furthermore,  it  appears  that  although 
under  these  conditions  the  psychical  stimulation  of  actual  riding  may 
possibly  be  conducive  to  greater  muscular  effort  at  the  time,  yet  this 
factor  does  not  necessarily  play  any  role  with  regard  to  the  efficiency  of  the 
body  as  a  machine.  The  subject  may  have  the  personal  impression  that 
the  work  done  upon  the  bicycle  ergometer  in  the  confines  of  the  laboratory 
or  inside  a  respiration  chamber  is  a  greater  strain  and  requires  more  phys- 
ical exertion  than  ordinary  bicycle  riding;  on  the  other  hand,  we  have 
no  evidence  to  indicate  that  experiments  made  upon  this  ergometer  are 
in  any  way  physiologically  abnormal.  Indeed,  the  absence  of  the  neces- 
sity for  balancing  or  steering  the  wheel  might  easily  lead  to  a  diminution 
of  the  extraneous  muscular  effort  incidental  to  outdoor  bicycle  riding, 
and  thus  result  in  a  larger  proportional  output  of  energy  due  to  the  leg 
muscles. 

In  using  the  bicycle  ergometer  the  subject  ordinarily  rides  for  half 
to  three-quarters  of  an  hour  before  the  actual  experiment  begins.  This 
is  more  for  the  purpose  of  establishing  a  physiological  equilibrium  in  the 
body  of  the  man  than  to  adjust  the  apparatus  to  any  particular  condition; 
during  this  period,  also,  there  is  a  warming  of  the  magnet  coil  to  a  con- 
stant temperature  and  likewise  a  heating  of  the  copper  disk  until  it  reaches 
a  point  when  the  heat  production  is  exactly  equal  to  the  heat  lost  through 


INTRODUCTION  9 

conduction  and  radiation,  so  that  the  temperature  of  the  copper  disk  re- 
mains essentially  constant. 

This  form  of  electric  brake  has  proved  particularly  advantageous,  in- 
asmuch as  it  is  at  ordinary  temperatures  absolutely  constant;  for  com- 
parison experiments,  in  which  the  same  individual  uses  the  apparatus 
under  differing  conditions  of  diet,  or  in  which  different  subjects  use  the 
same  apparatus,  the  results  are  especially  satisfactory,  since  a  definitely 
known  amount  of  muscular  activity  for  all  subjects  is  obtained.  Never- 
theless it  is  necessary  at  times  to  know  not  only  the  relative  but  also  the 
absolute  energy  value  of  the  work  done  upon  the  apparatus,  and  hence 
it  was  considered  desirable  to  calibrate  the  instrument  in  order  to  find 
in  absolute  units  the  heat  output  per  revolution  of  the  pedals. 

METHOD  OF  CALIBRATION. 

The  bicycle  ergometer  may  be  calibrated  in  a  number  of  ways.  Either 
a  cradle  dynanometer  can  be  used  or  the  rear  wheel  of  the  bicycle  can  be 
driven  by  means  of  a  belt  or  sprocket  chain,  or,  better  still,  by  a  gear 
or  direct-friction  drive;  but  these  methods  involve  so  many  and  so  large 
corrections  that  the  final  value  might  be  seriously  in  error.  A  method 
for  calibrating  this  type  of  instrument  suggested  by  the  late  Prof.  W.  0. 
Atwater  has  been  in  use  for  some  time  and  has  given  admirable  results. 
Professor  Atwater's  method  involved  placing  the  ergometer,  exactly  as 
it  was  to  be  used  for  an  experiment,  inside  of  a  respiration  calorimeter, 
and  driving  the  apparatus  from  the  outside  by  means  of  a  shaft,  magnet- 
izing the  field  as  desired.  The  number  of  revolutions  of  the  pedal  could 
then  be  counted  and  the  heat  directly  given  off  by  the  instrument  meas- 
ured as  in  an  ordinary  calorimeter  experiment.1 

This  method  of  calibration  was  extensively  employed  on  the  first 
apparatus  and  it  has  already  been  described.2  The  calorimeter  then 
used  was  the  original  respiration  calorimeter  in  the  chemical  laboratory 
of  Wesleyan  University  in  Middletown,  Connecticut.  This  calorimeter 
was  a  universal  apparatus,  inasmuch  as  with  it  experiments  could  be  made 
with  men  not  only  at  rest  but  also  undergoing  severe  muscular  work. 
The  apparatus  ^was  consequently  of  considerable  size.  While  the 
earlier  check-tests  showed  an  agreement  among  themselves  that  was  highly 
satisfactory,  certain  apparent  abnormalities  in  the  curve  of  calibration 
have  been  adversely  criticized  by  European  observers  in  private  communi- 
cations. The  earlier  calorimetric  calibrations  of  the  ergometer  indicated, 
for  example,  that  within  the  limits  of  speed  used,  namely,  from  55  to  85 
revolutions  per  minute,  the  heat  per  revolution  was  approximately  constant, 
with  the  same  degree  of  magnetization  in  the  field.  From  elementary 

1  It  is  interesting  to  recall  in  this  connection  that  Violle  (Comptes  rendus,  1870,  70, 
p.  1283)  many  years  ago  made  determinations  of  the  mechanical  equivalent  of  heat  by 
expending  a  known  amount  of  energy  in  rotating  a  disk  of  metal  between  the  poles  of  an 


electro-magnet  and  then  quickly  plunging  the  disk  into  a  water  calorimeter, 
enedict  and  Carpenter,  loc.  cit.,  p.  14. 


Ber 


10  A    BICYCLE    ERGOMETER   WITH   AN   ELECTRIC    BRAKE 

theoretical  considerations,  as  will  be  shown  in  the  third  section,  this  was 
not  what  would  be  expected;  it  appeared  desirable,  therefore,  to  repeat 
the  calibrations  with  a  more  delicate  respiration  calorimeter  subsequently 
constructed  in  the  Nutrition  Laboratory  at  Boston.  Through  the  cour- 
tesy of  Dr.  C.  F.  Langworthy,  of  the  U.  S.  Department  of  Agriculture, 
Washington,  D.  C.,  the  original  bicycle  ergometer  was  sent  to  Boston 
and  installed  inside  the  respiration  chamber,  fitted  with  a  crank-shaft, 
motor,  belting,  and  shafting,  and  rotated  at  the  varying  rates  of  speed 
formerly  used.  The  range  of  speed  was  then  considerably  altered  so  as 
to  secure  a  rate  of  revolution  of  the  pedals  as  low  as  11  and  as  high  as  120 
per  minute. 

When  the  new  bicycle  ergometer,  constructed  in  the  mechanical  de- 
partment of  the  Nutrition  Laboratory,  had  been  completed,  it  was  sub- 
jected to  similar  calibration  tests,  so  that  we  now  have  an  extensive  series 
of  calibration  tests  with  two  ergometers  of  this  type,  built  some  10  or  12 
years  apart,  having  different  electro-magnets  and  yet  embodying  the  same 
fundamental  principle.  The  next  section  of  this  report  gives  an  account 
of  these  calibration  tests,  while  in  the  third  section  a  study  is  made  of 
the  magnetic  reactions  that  take  place  when  the  disks  of  these  instru- 
ments are  in  rotation. 


PART   II. 


CALIBRATION  TESTS. 

The  calorimeter  used  for  the  later  calibration  tests  of  the  two  bicycle 
ergometers  was  the  so-called  chair  calorimeter,  which  has  been  described 
in  detail  by  Benedict  and  Carpenter.1  Since  this  description  was  pub- 
lished, it  has  been  found  desirable  to  change  the  location  of  the  entrance 
from  the  top  to  the  front  of  the  apparatus.  This  permits  the  easy  in- 
troduction of  the  ergometer  and  the  carrying  of  the  driving-shaft  straight 
out  from  the  front  of  the  calorimeter. 

The  apparatus  consists,  in  brief,  of  a  series  of  chambers  surrounded  by 
alternate  layers  of  air  and  insulating  materials.  The  inner  copper  cham- 
ber is  surrounded  by  a  layer  of  air,  in  which  is  located  the  structural-steel 
framework  of  the  calorimeter.  A  zinc  wall  incloses  this  air-space,  and  is 
in  turn  surrounded  by  a  second  air-space  of  approximately  8  cm.,  which 
is  inclosed  by  an  insulating  outer  layer  of  hair-felt,  with  a  final  covering 
of  asbestos.  Between  the  zinc  and  copper  walls  there  is  a  series  of  thermo- 
electric junctions  which  indicate  the  temperature  differences  between  the 
two.  By  arbitrarily  heating  or  cooling  the  air  between  the  hair-felt  and 
the  zinc  wall,  the  temperature  of  the  latter  can  be  controlled  at  will  and 
adjusted  so  that  it  will  be  equal  to  that  of  the  copper  wall,  thus  preventing 
any  heat  radiation  and  holding  the  calorimeter  adiabatic.  The  heat  given 
off  by  the  subject  is  absorbed  by  a  current  of  cold  water  passing  through 
a  system  of  brass  pipes  inside  the  chamber,  the  heat-absorbing  surface  of 
these  pipes  being  greatly  increased  by  a  large  number  of  copper  disks, 
approximately  5  cm.  in  diameter,  which  are  soldered  to  them.  The  rate 
of  flow  and  the  temperature  of  the  water  entering  the  chamber  are  ar- 
bitrarily adjusted  so  as  to  bring  away  the  heat  as  rapidly  as  it  is  produced. 
The  mean  temperature  of  the  air  in  the  calorimeter  is  thus  held  constant, 
this  being  the  criterion  of  the  thermal  equilibrium.  As  the  current  of 
water  enters  and  leaves  the  chamber  its  temperature  is  accurately  meas- 
ured with  mercurial  thermometers;  from  the  mass  and  rise  in  temperature 
of  the  water  the  amount  of  heat  brought  away  can  be  readily  computed. 
When  the  apparatus  is  used  for  calibrating  the  ergometer,  in  the  final 
calculation  of  the  total  intake  of  heat,  it  is  necessary  to  deduct  the  heat 
of  magnetization,  i.  e.,  the  heat  produced  in  the  coils  of  the  magnet.  As 
previously  stated,  this  is  with  the  first  ergometer  10.9  calories  per  hour 
when  the  magnetizing  current  is  1.25  amperes,  and  with  the  new  ergom- 
eter 17.8  calories  per  hour  when  the  magnetizing  current  is  1.5  amperes. 

1  Benedict  and  Carpenter,  Carnegie  Institution  of  Washington  Publication  No.  123. 
1910,  p.  10. 

11 


12  A    BICYCLE    EBGOMETER   WITH    AN    ELECTRIC    BRAKE 

When  placed  in  the  calorimeter,  the  ergometer  was  divested  of  the 
handle-bar  and  pedals,  and  usually  of  the  front  support.  Furthermore, 
in  order  to  secure  it  properly  inside  the  calorimeter,  it  was  necessary  to 
place  it  on  end.  This  position  is  shown  in  fig.  3.  A  somewhat  diagram- 
matical representation  of  the  electric  motor  and  of  the  pulley  systems 
used  to  reduce  the  speed  is  also  shown  in  the  lower  part  of  the  figure. 
In  actual  practice  the  motor,  instead  of  being  bolted  to  one  of  the  calorim- 
eter supports,  was  fastened  to  the  laboratory  floor.  A  separate  support 
for  the  pulleys  and  shafting  was  likewise  arranged  so  that  the  entire 
driving-mechanism  was  independent  of  the  calorimeter,  the  only  con- 
nection between  the  ergometer  and  the  driving-mechanism  being  the  long 
shaft  passing  out  through  a  small  hole  in  the  front  of  the  calorimeter. 
This  shaft  was  so  adjusted  as  to  have  free  clearance  at  all  points.  The 
temperature  of  the  calorimeter  room  was  also  carefully  controlled,  so 
that  it  would  be  equal  to  the  temperature  inside  the  calorimeter,  thus 
preventing  any  interchange  of  heat  along  the  metallic  shaft. 

By  means  of  an  adjustable  resistance  in  the  motor  circuit,  it  was  pos- 
sible to  regulate  the  speed  of  the  motor  so  as  to  have  the  rotation  of  the 
pedals  vary  from  11  to  120  per  minute.  The  particularly  low  speeds 
were  used  only  in  calibrating  the  new  ergometer,  being  especially  utilized 
for  studying  the  magnetic  conditions  in  the  field  during  calibration. 

THE  TECHNIQUE  OF  A  CALIBRATION  EXPERIMENT. 

In  order  to  bring  the  ergometer  and  the  calorimeter  into  temperature 
equilibrium,  a  preliminary  period  of  approximately  1  hour  was  necessary, 
during  which  time  the  ergometer  was  rotated  at  the  desired  speed,  the 
rate  of  flow  of  the  water-current  through  the  heat-absorbing  coils  inside 
the  calorimeter  adjusted,  and  the  temperature  of  the  calorimeter  regu- 
lated so  that  the  heat  brought  away  was  exactly  equal  to  the  heat  devel- 
oped by  the  ergometer.  The  current  through  the  magnet  was  likewise 
adjusted  to  constancy.  When  complete  temperature  equilibrium  had 
been  established,  the  experiment  proper  began.  An  automatic  counter 
recorded  the  number  of  revolutions  of  the  shaft  outside  the  chamber;  at 
the  exact  moment  of  beginning  the  period,  a  reading  of  this  counter  was 
taken,  the  current  of  water  to  bring  away  the  heat  was  deflected  into  a 
large  can  on  a  platform  balance,  so  that  the  amount  of  water  passing 
through  the  heat-absorbing  coils  could  be  accurately  weighed,  and  the 
initial  temperature  of  the  air  inside  the  calorimeter  was  carefully  recorded, 
all  of  these  records  being  continued  for  several  successive  series  of  1-hour 
periods.  Every  4  minutes  the  temperatures  of  water  entering  and  leaving 
the  chamber  were  recorded,  and  the  temperature  of  the  zinc  wall  was  ad- 
justed whenever  necessary  to  bring  it  to  the  temperature  of  the  copper 
wall,  so  as  to  maintain  adiabatic  conditions  throughout  the  whole  ex- 
periment. Usually  each  calibration  test  occupied  five  or  six  1-hour  pe- 
riods. At  the  end  of  the  experiment  the  calorimeter  door  was  opened 


CALIBRATION   TESTS 


.  3. — Scheme  for  calibration  of  the  ergometer  in  a  respiration  calorimeter.  The  ergometer,  divested 
of  handle-bars  and  seat,  is  placed  in  a  vertical  position  inside  a  respiration  chamber.  The  copper  disk 
D  rotating  between  the  pole-faces  P  of  the  electro-magnet  C  generates  heat  which  is  measured 
by  the  calorimeter.  The  electric  motor  and  reduction  pulleys  are  used  to  rotate  the  ergometer  at 
different  speeds  for  purposes  of  calibration. 


14  A   BICYCLE   ERGOMETER    WITH    AN    ELECTRIC    BRAKE 

quickly  and  the  temperature  of  the  copper  disk  recorded  by  placing  a 
mercurial  thermometer  upon  it,  a  rapid  conduction  of  the  heat  being  se- 
cured by  covering  the  bulb  of  the  thermometer  first  with  a  closely  fitting 
piece  of  sheet  lead  and  then  with  a  large  piece  of  cotton  batting.  As  soon 
as  the  mercurial  thermometer  reached  its  maximum  point  the  temperature 
was  recorded.  While  possibly  this  method  did  not  give  the  exact  tem- 
perature of  the  inner  part  of  the  copper  disk,  nevertheless  it  was  assumed 
that  the  record  obtained  could  be  considered  as  an  index  of  the  tem- 
perature of  the  copper  in  the  different  experiments.  These  readings  of 
temperature  were  taken  chiefly  for  comparison  with  the  magnetic  tests 
(see  Part  III).1 

Occasionally  it  was  possible  on  the  same  day  to  run  two  calibration 
tests,  either  at  two  different  speeds  or  at  two  different  intensities  of  field 
magnetization,  in  which  case,  immediately  after  taking  the  temperature 
of  the  copper  disk,  the  calorimeter  was  again  closed  and  the  second  pre- 
liminary period  run.  Under  these  conditions  it  was  usually  not  necessary 
that  the  second  preliminary  period  should  be  so  long  as  the  first  and  it 
was  possible  to  begin  the  measurements  on  the  second  basis  inside  of 
half  or  three-quarters  of  an  hour. 

CALIBRATION  TESTS  OF  ERGOMETER  I. 
EARLIER  CALIBRATION   TESTS. 

The  original  ergometer  (which  we  will  designate  as  ergometer  I)  was 
calibrated  frequently  in  the  large  respiration-chamber  at  Middletown, 
Connecticut,  in  1903,  1904,  and  1905.  These  calibrations  were  pub- 
lished by  Benedict  and  Carpenter  in  an  earlier  publication,2  but  they  are 
reproduced  here  in  table  1  with  some  slight  correction  and  rearrangement, 
so  that  they  may  be  readily  compared  with  the  results  of  the  later 
calibration  tests.  The  shortest  experiment  recorded  was  2  hours  and  21 
minutes  in  length  and  the  longest  7  hours  and  10  minutes,  the  strength 
of  current  through  the  ergometer  magnet  varying  from  0.70  ampere  to 
1.25  amperes.  Of  particular  significance  are  the  data  given  in  the  last 
two  columns  of  the  table,  showing  the  number  of  revolutions  per  minute 
and  the  heat  per  revolution.  It  will  be  observed  that  in  these  experi- 
ments the  lowest  number  of  revolutions  studied  was  71  per  minute  and 
the  highest  102,  those  for  1904  and  1905  ranging  almost  exclusively  be- 
tween 71  and  83  revolutions  per  minute.  The  heat  per  revolution  ranged 
from  0.0124  to  0.0236.  A  comparison  of  the  data  regarding  the  heat  per 
revolution  with  the  strength  of  current  used  in  the  various  tests  shows 
that  in  general  the  higher  the  magnetizing  current  the  higher  the  heat 
per  revolution. 

1  The  influence  of  the  temperature  of  surroundings  on  the  constancy  of  the  ergometer 
is  discussed  in  Part  III. 

2  Benedict  and  Carpenter,  U.  S.  Department  of  Agriculture,  Office  of  Expt.  Stas. 
Bui.  No.  208, 1909,  p.  16. 


CALIBRATION   TESTS 


15 


TABLE  1. — Results  of  earlier  calibration  tests  of  ergometer  I. 

[Experiments  made  in  the  respiration  calorimeter  at  Wesleyan  University,  Middletown,  Connecticut.] 


Date. 

Duration  of 
experiment. 

Cur- 
rent. 

Heat 

meas- 
ured. 

Corr.  for 
change 
ofcal. 
temp. 

Corr.  for 
heat  of 
magnet- 
ization. 

Heat 
pro- 
duced. 

Total 
no.  of 
revolu- 
tions of 
pedals. 

No.  of 
revolu- 
tions 
permin. 

Heat  per 
revolu- 
tion. 

1903. 

h.     m.       s. 

amp. 

CO/8. 

cafe. 

cals. 

cals. 

cals. 

Oct.     5 

6     17      6 

1.25 

774.8 

-3.6 

-68.7 

702.5 

29,967 

79 

0.0234 

6 

4    52    46  1  1.25 

743.4 

-9.0 

-53.4 

681.0 

30,006 

102 

.0227 

9 

6    50    34  !  1.25 

855.8 

-2.4 

-74.7 

778.7 

33,554 

82 

.0232 

12 

4    49    30     1.25  i  533.4 

-52.9  !  480.5 

20,837 

72 

.0231 

12 

4    20    30 

1.25 

637.8 

-47.4 

590.4 

25,833 

99 

.0229 

1904. 

Oct.   26 

7     10    50 

1.25 

874.5 

-78.6 

795.9 

34,158 

79 

.0233 

Nov.  18 

5    39    30 

1.25 

644.3 

+3.0 

-62.0 

585.3 

25,214 

74 

.0232 

18 

5     14    27 

1.25 

666.8 

+2.4 

-57.2 

612.0 

25,964 

83 

.0236 

1905. 

May  13 

6    30      0 

.80 

481.2 

+3.0 

-27.6 

456.6 

27,769 

71 

.0164 

15 

600 

.70 

359.1 

+  .6 

-19.4 

340.3 

27,361 

76 

.0124 

16 

600 

.90 

503.6 

+  .6 

-32.5 

471.7 

26,713 

74 

.0176 

17 

600 

1.25 

726.1 

+  .6 

-65.7 

661.0 

29,157 

81 

.0227 

18 

600 

.70 

381.3 

-19.4 

361.9 

27,290 

76 

.0133 

19 

600 

.80 

440.2 

-  '.6 

-25.5 

414.1 

26,532 

74 

.0156 

20 

600 

1.25 

746.3 

+  .6 

-65.6 

681.3 

29,958 

83 

.0227 

22 

2    21       0 

.90 

200.5 

-7.2 

-12.7 

180.6 

10,654 

76 

.0170 

23 

700 

.80 

521.0 

+2.4 

-29.7 

493.7 

31,586 

75 

.0156 

24 

700 

.90 

614.3 

-37.8 

576.5 

32,950 

78 

.0175 

26 

400 

.70 

252.5 

-13.0 

239.5 

19,227 

80 

.0125 

27 

700 

1.25 

837.4 

-4.2 

-76.6 

756.6 

32,945 

78 

.0230 

29 

600 

.70 

394.8 

+  .6 

-19.4 

376.0 

28,899 

80 

.0130 

29 

600 

1.10 

671.3 

-   .6 

-50.5 

620.2 

30,035 

83 

.0207 

CALIBRATION  TESTS  OF  1911. 

An  extensive  series  of  calibration  tests  of  ergometer  I  was  carried  out 
at  the  Nutrition  Laboratory  in  June  and  July  of  1911.  The  details  of  a 
single  day's  experiment,  that  of  July  7, 1911,  will  serve  to  show  the  method 
used  in  these  tests.  While  the  results  of  the  experiments  are  usually 
expressed  in  totals  for  3  to  6  hours,  the  particular  experiment  selected 
was  run  in  a  series  of  six  1-hour  periods,  and  the  individual  hourly  de- 
terminations are  given  in  table  2.  Even  when  experimental  periods  are 
longer  than  1  hour,  computations  made  on  the  hourly  basis  are  frequently 
of  much  value  in  indicating  abnormalities  in  the  course  of  an  experiment; 
usually  these  periods  agree  very  satisfactorily  with  each  other. 

The  weight  of  water  passing  through  the  heat-absorbing  system  during 
the  experimental  period  and  the  rate  of  flow  per  minute  are  first  recorded, 
then  the  average  temperature  difference  between  the  water  entering  and 
that  leaving  the  chamber,  with  a  slight  correction  suggested  as  necessary 
by  Armsby1  for  the  pressure  of  water  upon  the  glass  bulbs  of  the  ther- 
mometers, the  final  corrected  temperature  difference  being  also  given. 
Multiplying  the  weight  of  water  by  this  corrected  temperature  difference 
gives  the  heat  measured  in  terms  of  large  calories.  A  further  correction 

1  Armsby,  U.S.  Dept.  Agr.,  Bureau  of  Animal  Industry  Bui.  51,  1903,  p.  34;  Atwater 
and  Benedict,  Carnegie  Institution  of  Washington  Publication  No.  42,  1905,  p.  134. 


16 


A    BICYCLE    ERGOMETER   WITH    AN    ELECTRIC    BRAKE 


is  necessary  for  the  changes  in  temperature  of  the  calorimeter.  Since  an 
increase  or  decrease  in  temperature  indicates  a  storage  or  loss  of  heat, 
it  is  necessary  to  add  or  subtract  the  heat  thus  stored  or  lost  to  find  the 
amount  of  heat  actually  produced  during  the  experimental  period.  The 
heat  produced  by  the  current  passing  through  the  magnet  amounted  to 
10.9  calories  per  hour,  the  third  and  fourth  periods  in  the  table  being  re- 
spectively 1  minute  shorter  and  1  minute  longer  than  the  hour,  thus  ac- 
counting for  the  slight  variations  from  the  average.  The  total  heat 
produced,  then,  is  the  heat  measured,  corrected  for  the  changes  in  tem- 
perature of  the  calorimeter  and  for  the  heat  produced  by  the  magnetizing 
current.  The  records  of  the  total  number  of  revolutions  per  hour  as 
obtained  from  the  revolution  counter  are  given,  together  with  the  num- 
ber of  revolutions  per  minute.  The  final  column  indicates  the  number  of 
calories  of  heat  produced  per  revolution  of  the  pedals. 


TABLE  2— Results  of  calibration  test  of  ergometer  I,  July  7,  1911. 

[Current  in  ergometer  magnet,  1.25  amperes.] 


Duration  of  period. 

Weight  of 
water. 

Avg. 
rate  per 

min. 

Avg. 
temp, 
diff. 

Corr.  for 
pressure 
on  bulbs. 

Corr. 

IT 

10h22ma.m.  to  Ilh22ma.m 

MM. 

35.09 
34.81 
34.58 
33.91 
34.72 
34.07 

C.  C. 

585 
580 
576 
575 
569 
568 

°C. 

3.03 
3.11 
3.04 
3.12 
3.16 
3.13 

•C. 

+0.02 
+  .01 
+  .01 
+  .01 
+  .01 
+  .01 

"C. 

3.05 
3.12 
3.05 
3.13 
3.17 
3.14 

11  22  a.m.  to  12  22  p.m. 
12  22  p.m.  to    1  22  p.m  . 
1  22  p.m.  to    2  21  p.m.1 
2  21  p.m.  to    3  22  p.m.2 
3  22  p.m.  to    4  22  p.m  . 

10  22  a.m  to    4  22  p.m  

207.18 

575 

3.10 

+.01 

3.11 

Duration  of  period. 

Heat 
measured. 

Corr.for 
change 
of  cal. 
temp. 

Corr.  for 
heat  of 
magnet- 
ization. 

Heat 
pro- 
duced. 

No.  of 

revolu- 
tions of 
pedals. 

No.  of 
revolu- 
tions 
permin. 

Heat  per 
revolu- 
tion. 

10h22'°a.m.  to  Ilh22ma.m. 
11  22  a.m.  to  12  22  p.m. 
12  22  p.m.  to    1  22  p.m. 
1  22  p.m.  to    2  21  p.m.1 
2  21  p.m.  to    3  22  p.m.2 
3  22  p.m.  to    4  22  p.m. 

10  22  a.m.  to    4  22  p.m  . 

cals. 

107.0 
108.6 
105.5 
106.1 
110.1 
107.0 

cals. 
+0.6 
-    .6 
+  1.5 

+  .2 
-1.8 

cals. 
-10.9 

-10.9 
-10.9 
-10.7 
-11.1 
-10.9 

cals. 
96.7 

97.1 
96.1 
95.6 
97.2 
96.1 

4,306 
4,264 
4,278 
4,196 
4,300 
4,246 

72 
71 
71 
71 
70 
71 

cal. 
0.0225 
.0228 
.0225 
.0228 
.0226 
.0226 

644.3 

-65.6 

578.7 

25,590 

71 

.0226 

•  59  minutes  long. 


2  61  minutes  long. 


During  the  experiment  of  July  7,  1911,  the  heat  per  revolution  of  the 
pedals  ranged  only  from  0,0225  to  0.0228  calorie  per  revolution,  the 
average  for  the  whole  experiment  being  0.0226  calorie  per  revolution. 
The  average  number  of  revolutions  during  the  test  was  71.1  per  minute. 
With  this  ergometer,  therefore,  with  a  current  of  1.25  amperes  through  the 
magnet,  it  can  be  stated  that  at  this  speed  each  revolution  results  in 
the  development  of  0.0226  calorie. 


CALIBRATION   TESTS 


17 


TABLE  3. — Results  of  later  calibration  tests  of  ergometer  I. 

[Experiments  made  in  the  chair  calorimeter  at  the  Nutrition  Laboratory,  Boston,  Massachusetts.] 


Date. 

Duration  of 
experiment. 

Cur- 
rent. 

Heat 

meas- 
ured. 

Corr.  for 
change 
of  cal. 
temp. 

Corr.  for 
heat  of 
magneti- 
zation. 

Heat 
pro- 
duced. 

No.  of 
revolu- 
tions of 
pedals. 

No.  of 
revolu- 
tions 
per 
minute 

Heat 
per 
revolu- 
tion. 

1911. 

h.       m.      s. 

amp. 

cafe. 

cals. 

cola. 

cols. 

cal. 

June  7 

500 

1.25 

592.9 

—0.2 

—54.7 

538.0 

23,245 

77 

0.0231 

8 

300 

1.25 

253.6 

—   .6 

—32.8 

220.2 

10,071 

56 

.0219 

9 

4    57    53 

1.25 

275.1 

—   .2 

—54.3 

220.6 

11,600 

39 

.0190 

12 

400 

1.10 

426.7 

—33.9 

392.8 

18,383 

77 

.0214 

15 

400 

1.10 

187.2 

—  '.4 

—33.9 

152.9 

8,824 

37 

.0173 

16 

300 

1.10 

250.1 

—  .2 

—25.4 

224.5 

10,861 

60 

.0207 

26 

400 

.90 

359.1 

—22.7 

336.4 

19,962 

83 

.0169 

27 

6      00 

.90 

397.7 

—  '.8 

—34.0 

362.9 

20,680 

57 

.0175 

28 

400 

.90 

422.9 

—  .2 

—22.7 

400.0 

26,135 

109 

.0153 

30 

300 

1.10 

424.9 

+   .2 

—25.4 

399.7 

21,739 

121 

.0184 

July    3 

300 

1.25 

429.4 

+   .4 

—32.8 

397.0 

18,006 

100 

.0220 

6 

300 

1.25 

483.9 

—  .2 

—32.8 

450.9 

21,494 

119 

.0210 

7 

600 

1.25 

644.3 

—65.6 

578.7 

25,590 

71 

.0226 

8 

300 

.80 

279.2 

—13.4 

265.8 

21,982 

122 

.0121 

10 

300 

.90 

340.0 

+  '.2 

—17.0 

323.2 

21,928 

122 

.0147 

11 

300 

.90 

325.9 

4 

—17.0 

308.5 

20,729 

115 

.0149 

12 

300 

.90 

169.1 

—17.0 

152.1 

8,941 

50 

.0170 

13 

500 

.70 

297.8 

—  .2 

—17.1 

280.5 

22,461 

75 

.0125 

14 

300 

.80 

222.5 

—  .8 

—13.4 

208.3 

13,272 

74 

.0157 

15 

300 

.70 

182.4 

—  .2 

—10.3 

171.9 

13,964 

78 

.0123 

18 

300 

.90 

124.5 

+   .6 

—17.0 

108.1 

7,108 

39 

.0152 

20 

2    59    25 

.90 

356.6 

—  .4 

—16.9 

339.3 

27,463 

153 

.0124 

The  results  of  all  of  the  later  tests  of  ergometer  I,  made  with  the  chair 
calorimeter  at  the  Nutrition  Laboratory,  Boston,  Massachusetts,  are 
given  in  table  3,  the  averages  alone  being  recorded.  Special  attention 
is  again  directed  to  the  column  indicating  the  number  of  revolutions  of 
the  pedals  per  minute  and  the  heat  per  revolution.  While  it  will  be 
remembered  that  in  the  earlier  tests  the  rate  of  revolution  of  the  pedals 
varied  only  between  narrow  limits,  i.e.,  from  70  to  90,  here  we  find  values 
as  low  as  37  revolutions  per  minute  and  as  high  as  153. 

While  no  bicyclist  could  be  expected  to  ride  at  the  enormous  speed  of 
153  revolutions  of  the  pedals  per  minute,  it  may  be  interesting  to  note 
that  a  professional  bicycle  rider,  who  has  been  recently  experimented  upon 
in  this  laboratory,  has  repeatedly  maintained  speeds  of  130  to  140  revolu- 
tions per  minute  for  2  minutes  at  a  time  during  a  spurt;  in  fact,  in  ex- 
periments with  men,  much  difficulty  has  been  experienced  in  securing  a 
low  rate  of  speed.  The  tests  with  abnormal  rates  of  speed  are,  however, 
included  more  for  the  purpose  of  studying  the  peculiar  relationship  re- 
cently noted  between  the  revolutions  per  minute  and  the  heat  produced 
per  revolution.  An  examination  of  the  results  in  table  3  again  shows  that, 
in  general,  as  would  be  expected,  the  greater  the  heat  produced  by  the 
magnetizing  current  the  greater  the  heat  per  revolution. 

For  an  adequate  study  of  the  relationship  between  the  number  of  revo- 
lutions per  minute  and  the  heat  per  revolution,  it  was  advisable  to  ex- 
press the  calibrations  for  the  different  strengths  of  current  through  the 


18 


A   BICYCLE   ERGOMETER   WITH   AN   ELECTRIC    BRAKE 


field  in  the  form  of  curves.  Accordingly,  in  fig.  4  we  have  all  of  the  ex- 
periments made  with  ergometer  I  with  a  current  through  the  armature  of 
0.70  and  0.80  ampere.  On  this  diagram  the  points  indicated  by  circles  are 
those  obtained  with  the  earlier  calibrations  with  this  ergometer,  of  which 
the  results  are  given  in  table  1.  The  values  indicated  by  small  crosses 
are  those  obtained  in  the  tests  during  June  and  July  of  1911  (see  table  3). 


.017 
.016 
.015 

.014 

.013 
.012 


6O       7O       80       9O       1OO      11O      12O 

Fio.  4. — Heat  per  revolution  of  ergometer  I  for  currents  of  0.7 
and  0.8  ampere  through  field.  Ordinates  represent  heat  per 
revolution  expressed  in  large  calories.  Abscissae  represent 
revolutions  per  minute. 

In  practically  all  of  the  experiments  made  with  a  current  of  0.70  am- 
pere, it  will  be  seen  that  the  average  speed  ranged  between  75  and  82 
revolutions  per  minute,  and  that  the  variations  in  heat  per  revolution 
are  not  very  great.  Four  of  the  five  experiments  made  with  0.80  am- 
pere through  the  field  were  between  the  limits  of  71  and  75  revolutions 
per  minute,  and  hence  these  values  were  all  clustered  around  one  point. 
Of  particular  interest  is  the  fact  that  the  fifth  experiment  was  made  with 
122  revolutions  per  minute,  and  in  this  experiment  we  find  that  the  heat 
per  revolution  was  considerably  less  than  when  the  speed  was  71  to  75 
revolutions. 

In  the  earlier  tests  of  this  ergometer,  practically  all  of  the  experimental 
evidence  was  accumulated  at  a  speed  which  was  found  to  be  the  most 
practicable  and  comfortable  for  the  subject,  namely,  from  65  to  80  revo- 
lutions per  minute.  On  the  basis  of  these  calibrations  it  was  believed 
that  the  evidence  showed  that  the  heat  per  revolution  was  constant, 
irrespective  of  speed;  accordingly  it  is  of  interest  to  note  that  all  of  the 
experiments  with  a  current  of  0.70  ampere,  and  four  of  the  five  experi- 
ments with  0.80  ampere,  show  essentially  this  feature,  namely,  that  within 
narrow  limits  the  results  are  grouped  around  a  certain  value  which  is 
practically  independent  of  the  speed.  On  the  other  hand,  we  find  that 
in  the  experiment  with  a  very  high  speed  and  a  current  of  0.80  ampere 
there  is  a  greatly  decreased  heat  per  revolution. 

In  fig.  5  are  shown  the  values  obtained  with  a  current  of  0.90  ampere. 
With  this  current  the  experiments  are  much  more  numerous  and  include, 


CALIBRATION    TESTS 


19 


as  before,  both  the  earlier  calibrations  with  this  ergometer  and  those  of 
1911.  The  speed  varied  from  39  to  153  revolutions,  the  circles  indicating, 
as  before,  the  earlier  observations,  and  the  small  crosses  those  that  have 
recently  been  made.  The  plotting  of  these  points  shows  a  sharply  de- 
fined curve  with  a  striking  dissimilarity  between  the  rate  of  revolution 
and  the  heat  production  per  revolution.  This  distinctly  contradicts 
the  statement  previously  made  that  the  heat  per  revolution  was  independ- 
ent of  the  rate  of  speed.  With  a  low  rate  of  speed,  the  heat  per  revolu- 
tion is  likewise  low,  rises  to  a  maximum  when  the  speed  is  not  far  from  60 


.01  7 
.01  6 
.015 
.01  4 
.01  3 

^ 

-. 

^o 

/ 

*x 

X 

- 

/ 

X 

N 

x, 

X 

x 

\ 

X 

40       5O       60       7O       8O       9O      1OO      11O     12O     13O     14O     15O 

FIG.  5.  —  Calibration  curve  of  ergometer  I  for  magnetizing  current  of  0.9  ampere. 


X 

.021 

—^^ 

-      —  . 

"-»<_ 

/ 

o       • 

X 

.019 

/ 

\ 

X 

/ 

\ 

1 

If 

.018 
O1  7 

i 

30       40       5O       6O       7O       8O       9O 

FIG.  6. — Calibration  curve  of  ergometer  I  for  magnetizing  current  of  1.1  amperes. 

to  80  revolutions  per  minute,  and  gradually  falls  off  with  increasing  speed 
until,  with  a  speed  of  153  revolutions  per  minute,  it  is  even  lower  than 
at  the  very  low  rate  of  39  revolutions  per  minute.  It  is  of  especial  im- 
portance to  note  that  the  top  of  the  curve  is  obtained  when  the  speed  is 
from  55  to  80  revolutions  per  minute. 

Since  it  was  highly  improbable  that  all  subjects  would  wish  to  ride  the 
bicycle  ergometer  with  exactly  the  same  degree  of  resistance,  the  cal- 
ibrations were  made  so  extensive  as  to  cover  practically  all  of  the  different 


20 


A    BICYCLE    ERGOMETER   WITH    AN    ELECTRIC    BRAKE 


variations  in  resistance  that  could  be  experienced.  The  values  obtained 
in  five  tests  with  a  current  having  a  strength  of  1.1  amperes  are  presented 
in  fig.  6,  only  one  of  these  observations  being  made  in  the  earlier  cali- 
bration tests.  The  general  trend  of  this  curve  has  a  striking  similarity 
to  that  observed  with  a  strength  of  current  of  0.90  ampere. 

By  far  the  greater  number  of  the  work  experiments  performed  with 
ergometer  I  and  published  in  the  earlier  report  were  made  with  a  current 
through  the  field  of  1.25  amperes,  and  hence  in  the  later  calibration  tests 
of  this  instrument,  especial  care  was  taken  to  secure  values  at  different 
rates  of  speed  with  this  strength  of  current.  On  fig.  7  are  plotted  the 
points  for  the  earlier  observations  ranging  between  the  speeds  of  72  and 
102;  these  are  more  or  less  grouped  about  the  high  point  of  the  curve, 
which  is  somewhat  flat,  and  therefore  again  gives  justification  for  the 
assertion  that  the  heat  per  revolution  is  constant  irrespective  of  speed 
between  70  and  100  revolutions  per  minute.  The  points  determined 
in  ihe..  later  calibrations,  with  the  speed  varying  from  39  to  119  revolu- 
tions, indicate  the  same  general  form  of  curve,  with  a  maximum  between 
70  to  90  revolutions  per  minute. 


.024 
.023 
.02  2 
.021 
.020 
.019 

.^ 

0 

-Q  

/ 

• 

00 

^ 

o 

7 

N 

/ 

f 

s 

/ 

'SO       4O       5O       6O       70       8O       9O       tOO      11O      12O 

Fio.  7. — Calibration  curve  of  ergometer  I  for  magnetizing  current  of  1.25  amperes. 

It  is  a  matter  of  some  interest  that  all  of  the  more  recently  determined 
points  are  slightly  lower  than  those  determined  in  the  earlier  observations. 
While  this  is  not  strikingly  shown  in  the  preceding  curves,  it  is  possibly 
due  to  the  fact  that  the  apparatus  may  have  been  a  little  better  lubricated 
during  the  last  test,  since  it  had  been  put  in  thorough  working  condition 
after  several  years  of  use  and  a  smaller  and  more  accurate  calorimeter 
was  used.  Furthermore,  certain  of  the  earlier  friction  tests  appear  to 
show  that  the  apparatus  was  distinctly  not  so  free  from  friction  as  it  should 
have  been,  since  the  later  friction  tests  indicated  a  very  much  smaller 
value  than  that  originally  found.  It  should  be  stated,  however,  that  the 
two  friction  tests  made  and  reported  in  the  earlier  publication  were  by 
no  means  sufficient  in  number  or  extent  to  justify  definite  conclusions. 


CALIBRATION    TESTS 


21 


The  general  trend  of  these  curves  can  best  be  compared  by  plotting 
them  all  in  one  diagram,  and  in  fig.  8  this  has  been  done.  The  marked 
uniformity  in  the  general  trend  of  the  curves  is  obvious,  showing  that 
with  a  speed  between  65  and  90  revolutions  the  heat  per  revolution  is 
nearly  constant.  Below  60  and  above  90  the  heat  per  revolution  is 
considerably  less.  Since  in  the  series  of  calibrations  previously  published 
the  speed  ranged  only  between  60  and  90  or  100,  these  extreme  variations 
in  the  heat  per  revolution  were  not  observed,  and  not  until  these  later 
tests  were  made  did  they  appear.  They  naturally  provoke  discussion 
and  awaken  much  interest. 


.024 
.023 
.022 
.021 


.016 


.015 


.013 


.012 


\ 


3O       4O       5O       6O       7O       SO       9O       1OO      11O     12O     13O     14O     ISO 
FIG.  8. — Calibration  curves  of  ergometer  I  for  magnetizing  current  of  0.7  to  1.25  amperes. 

FRICTION  TESTS  WITH  ERGOMETER  I. 

Since  in  certain  experiments  when  a  man  is  riding  the  machine  the 
work  of  "coasting"  is  to  be  measured,  a  determination  of  the  internal 
friction  of  the  machine  is  desirable.  The  determination  is  made  by 
rotating  the  shaft  at  the  desired  speed  but  without  exciting  the  magnet. 

A  great  fault  in  the  earlier  tests  with  this  instrument  lay  in  the  fact 
that  the  friction  tests  were  made  under  extremely  adverse  conditions. 
To  measure  a  heat  production  of  approximately  2  calories  per  hour  with 
an  apparatus  designed  to  measure  not  less  than  50  calories  and  as  high 
as  625  calories  per  hour,  naturally  introduced  an  enormous  percentage 


22 


A    BICYCLE    ERGOMETER   WITH   AN   ELECTRIC    BRAKE 


error.  The  value  reported  by  Benedict  and  Carpenter,1  as  found  in  the 
one  experiment  made,  was  0.001547  calorie  per  revolution.  This  repre- 
sents about  8  per  cent  of  the  total  heat  per  revolution  with  a  current  of 
1.25  amperes.  Unwarranted  use  of  this  figure  was  made  by  the  authors 
in  their  discussion  of  the  problems  involved  in  experiments  on  men,  but 
the  best  data  then  available  were  used.  That  this  value  was  always  too 
high  seems  obvious,  and  at  the  earliest  opportunity  a  measurement  of 
the  heat  of  friction  given  off  by  this  machine  was  made  in  the  chair 
calorimeter  at  the  Nutrition  Laboratory.  The  results  of  two  experiments 
in  June  1911  are  given  in  table  4. 

TABLE  4. — Results  of  friction  tests  of  ergometer  I. 

[Magnet  not  excited.] 


Date  and  length  of  experiment. 

Heat 

meas- 
ured 

Corr.  for 
oft6 

Heat 
pro- 
duced 

No.  of 
revolu- 
tions of 

No.  of 
revolu- 
tions 

Heat  per 
revolu- 

temp. 

pedals. 

per  nun. 

cols. 

cats. 

caU. 

cal. 

1911,  June  13,  Ilh00n>a.m.  to  Ih00mp.m. 
June  14,  12  12  p.m.  to  5  12  p.m. 

3.8 

7.4 

+0.4 
-1.4 

4.2 

6.0 

15,308 
38,100 

128 
127 

0.000274 
.000157 

These  values,  while  by  no  means  as  concordant  as  could  be  desired, 
are  but  approximately  one-fifth  to  one-tenth  of  that  found  in  the  single 
test  made  in  Middletown,  Connecticut.  Subsequent  tests  made  with 
ergometer  II  (see  p.  29)  indicate  that  these  values  are  probably  not  far 
from  correct,  though  it  should  be  stated  that  a  calorimeter  designed  to 
measure  the  heat  production  of  a  man  is  not  best  adapted  to  measuring 
so  small  an  amount  as  1  or  2  calories  per  hour. 

Exactly  what  use  of  this  value  is  justified  in  an  experiment  with  a  man 
it  is  not  the  province  of  this  paper  to  discuss.  These  tests  are  given 
primarily  to  show  that  the  earlier  value  was  entirely  wrong  and  hence  all 
calculations  made  with  it  should  be  regarded  as  worthless. 

CALIBRATION  TESTS  OF  ERGOMETER  II. 

The  second  ergometer  was  constructed  during  the  summer  of  1911 
and,  after  preliminary  tests  as  to  the  winding  of  the  magnets,  the  ap- 
paratus was  substantially  installed  in  the  chair  calorimeter  for  a  series 
of  tests.  These  tests  covered  wide  ranges  of  speed  and  magnetizing 
current.  A  further  variant  was  introduced  in  that  in  some  of  the  ex- 
periments the  relative  position  of  the  disk  and  pole-faces  was  changed 
so  that  the  disk  rotated  much  nearer  one  pole-face  than  the  other.  Sub- 
sequently, the  entire  magnet  was  moved  towards  the  hub  in  a  straight 
line,  so  that  in  a  few  experiments  the  pole-faces  were  nearer  the  hub  by 
about  20  mm.  In  this  new  position  the  disk  was  at  times  in  the  center 
of  the  space  between  the  pole-faces  and  at  other  times  it  was  as  near  as 
possible  to  one  of  the  pole-faces  without  actual  contact  with  it.  These 
tests  with  varying  positions  of  the  magnet  were  all  incidental  to  a  study 

1  Benedict  and  Carpenter,  loc.  cit.,  p.  15. 


CALIBRATION   TESTS 


23 


of  the  peculiar  behavior  of  the  magnetic  field  when  the  copper  disk  was 
rotated  at  different  speeds.  The  results  of  the  several  calibration  tests 
are  reported  in  abstract  in  table  5. 

TABLE  5. — Results  of  calibration  tests  ofergometer  II. 


Date. 

Duration 
of 
period. 

Cur- 
rent. 

Heat 
meas- 
ured. 

Corr.  for 
change  of 
calorime- 
ter temp. 

Corr.  for 
heat  of 
magneti- 
Nation. 

Heat 
pro- 
duced. 

No.  of 
revolu- 
tions of 
pedals. 

No.  of 
revolu- 
tions 
per  min. 

Heat  per 
revolu- 
tion. 

1911. 

h.      m. 

amp. 

cols. 

cols. 

cals.        :     cats. 

cal. 

Oct.  28 

5      0 

1.25 

636.6 

-0.2 

—  60.8  ;  575.6 

36,148 

120 

0.0159 

30 

6      0 

1.25 

621.1       +  .2 

—  72.7    548.6 

29,072 

81 

.0189 

31 

6      0 

1.35 

705.5 

-   .2 

—  85.8    619.5 

29,228 

81 

.0212 

Nov.  1 

6      0 

1.50 

761.6 

+2.1 

—107.3    656.4 

29,947 

83 

.0219 

2 

6      0 

1.50 

563.3 

+  .4 

—106.9    456.8 

21,100 

59 

.0216 

3 

5      0 

1.50 

716.2 

+2.1 

—  89.1    629.2 

30,228 

101 

.0208 

4 

6      0 

1.50 

937.1 

-  .8 

—106.9    829.4 

42,438 

118 

.0195 

6 

6      0 

1.35 

490.7 

+  1.8      —  85.4    407.1 

20,834 

58 

.0195 

7 

6      0 

1.35 

752.5 

+  .4 

—  85.4    667.5 

36,376 

101 

.0184 

8 

6      0 

1.35 

834.4 

-f  .2      —  85.1     749.5 

42,870 

119 

.0175 

9 

6      0 

.25 

455.9 

-  .6      —  72.4    382.9 

20,858 

58 

.0184 

10 

3      0 

1.25 

356.5 

+  .2      —  36.2    320.5 

18,471 

103 

.0174 

10 

3      0 

.25 

345.1 

-   .4 

—  36.2 

308.5 

17,119 

95 

.0180 

11 

6      0 

1.10 

629.5 

—  55.2 

574.3 

43,832 

122 

.0131 

13 

6      0 

1.10 

581.6 

+Y.8 

—  55.2 

528.2 

36,573 

102 

.0144 

14 

6      0 

1.10 

489.9 

-1.0 

—  55.2 

433.7 

27,638 

77 

.0157 

15 

6      0 

1.10 

417.2 

—  55.5 

361.7 

21,853 

61 

.0166 

16 

6      0 

1.35 

655.2 

+".4 

—  85.4    570.2     28;840 

80 

.0198 

17 

6      0 

1.35 

767.8 

+1.6 

—  85.0    684.4     37,052 

103 

.0185 

20 

4      0 

1.50 

377.4 

+0.2 

—  70.9    306.7 

14,300 

60 

.0214 

21 

6      0 

1.50 

588.8 

-1.4 

—106.4    481.0 

21,888 

61 

.0220 

22 

5      0 

.95 

251.8 

+  .6 

—  34.0    218.4 

15,932 

53 

.0137 

23 

6      0 

.95 

293.7 

+  .4      —  40.8    253.3 

18,739 

52 

.0135 

24 

4      0 

1.50 

195.3 

+  1.4      —  71.2  !  125.5 

7,821 

33 

.0160 

25 

6      0 

1.50 

381.3 

+2.9 

—106.8  1  277.4 

15,186 

42 

.0183 

Dec.    1 

6      0 

1.35 

362.7 

-   .2 

—  85.4    277.1 

15,162 

42 

.0183 

2 

6      0 

1.25 

329.8 

+2.3 

—  72.0 

260.1 

14,945 

42 

.0174 

4 

6      0 

.95 

441.9 

—  40.8 

401.1 

27,502 

76 

.0146 

5 

6      0 

.95 

519.3 

+1.6 

—  40.9 

479.4 

36,311 

101 

.0132 

6 

6      0 

.95 

548.8 

-   .2 

—  40.8 

507.8     44,232 

123 

.0115 

7 

6      0 

1.10 

587.9 

+  .6 

—  55.7 

532.8  1   30,389 

84 

.0175 

8 

6      0 

1.10 

638.7 

+  .6 

—  55.7 

583.6     37,880 

105 

.0154 

9 

6      0 

1.10 

476.4 

+  .8 

—  55.6 

421.6     24,020 

67 

.0176 

11 

6      0 

1.25 

492.5 

+  .2 

—  72.4    420.3     22,554 

63 

.0186 

12 

5      0 

1.25 

507.1 

-   .2 

—  60.3  |  446.6  i   23,577 

79 

.0189 

12 

3      0 

1.25 

180.2 

-   .4 

—  36.2 

143.6       8,173 

45 

.0176 

13 

6      0 

1.25 

725.9 

+  .8 

—  72.4 

654.3 

39,910 

111 

.0164 

1912. 
Jan.    1 

4      0 

1.25 

284.8 

-1.4      —  48.5 

234.9 

11,987 

50 

.0196 

1 

4      0 

1.25 

451.0 

+6.2      —  48.5 

408.7     21,630 

90 

.0189 

1 

4      0 

1.25 

496.2 

+3.9 

—  48.5 

451.6     26,482 

110 

.0170 

6 

5      0 

1.25 

341.8 

+  1.4      —  60.6 

282.6     14,880 

50 

.0190 

9 

5      0 

1.25 

340.7 

-3.3      —  60.6 

276.8     13,970 

47 

.0198 

11 

5      0 

1.25 

317.9 

+2.5      —  60.6 

259.8     13,753 

46 

.0189 

15 

5      0 

1.25 

443.9 

+  .8      —  60.6 

384.1      18,232 

61 

.0211 

17 

5      0 

1.25 

636.5 

+2.0      —  60.6    577.9     32,937 

110 

.0175 

18 

5      0 

1.25 

473.6 

-   .4      —  60.3    412.9     21,791 

73 

.0189 

19 

5      0 

1.25 

508.4 

-1.8 

—  60.6    446.0     22,335 

74       .0200 

19 

5      0 

1.25 

294.9 

-4.1 

—  60.6     230.2     12,682 

42       .0182 

20 

4      0 

1.25 

414.1 

+2.5 

—  48.0 

368.6  |   19,124 

80       .0193 

20 

5      0 

1.25 

471  .4 

-  .2 

—  60.3 

410.9     21,039 

70    !    .0195 

21 

3    46 

1.25 

456.4 

+1.2 

—  45.4 

412.2  i   22,909 

101    i    .0180 

21 

5      0 

1.25 

610.0 

+  .4 

—  60.3 

550.1      30,283 

101 

.0182 

22 

5      0 

.95 

465.5 

-   .4 

—  34.0 

431.1      36,949 

123 

.0117 

22 

5      0 

.95 

462.2 

—  .8 

—  34.0    429.0 

37.482       125        .0114 

24 


A    BICYCLE    ERGOMETER   WITH    AN    ELECTRIC    BRAKE 


With  ergometer  I  the  magnetizing  current  ranged  from  0.70  ampere 
to  1.25  amperes,  but  inasmuch  as  the  winding  of  the  magnet  in  ergometer 
II  was  somewhat  different,  the  current  ranged  from  0.95  ampere  to  1.50 
amperes  in  the  calibration  tests  of  this  ergometer.  It  was  planned  to 
secure  calibrations  of  the  ergometer  at  each  current  with  variations  in 
speed  ranging  from  approximately  50  to  120  revolutions  of  the  pedals 
per  minute.  For  a  given  speed,  the  highest  values  of  heat  per  revolution 
were  obviously  found  with  the  largest  magnetizing  current,  namely,  1.50 
amperes.  As  a  matter  of  fact,  however,  the  experiments  of  November 
4  and  6  show  that  with  less  current  (1.35  amperes)  through  the  field- 
coils  but  with  a  low  speed,  the  heat  per  revolution  was  exactly  the  same 
as  with  a  current  of  1.50  amperes  and  with  twice  the  number  of  revolu- 
tions, namely,  118  revolutions  per  minute.  It  is  impossible,  however, 
to  analyze  satisfactorily  the  varying  conditions  without  recourse  to  a 
series  of  curves  plotted  for  each  intensity  of  magnetizing  current. 


01  b 
.01  4 
.01  3 
.012 
nil 

^ 

X-. 

^ 

~? 

\ 

v 

\ 

N 

K 

FIG.  9. — Calibration  curve  of  ergometer  II  for  magnetizing  current  of  0.95  ampere. 


.018 
.017 
.01 6 
.015 
.014 


6O       7O       8O       9Q       1OO      11O      12O 
Fio.  10. — Calibration  curve  of  ergometer  II  for  magnetizing  current  of  1.10  amperes. 

Beginning  with  the  lowest  current,  namely,  0.95  ampere,  we  find  that 
the  values  all  lie  fairly  close  to  the  curve  (see  fig.  9).  Two  of  the  obser- 
vations shown  on  this  curve  were  made  when  the  disk  was  rotating  very 
close  to  the  rear  pole,  leaving  a  wide  air-gap  on  the  other  side.  These 
two  values,  which  are  indicated  by  small  circles,  lie  approximately  on  the 


CALIBRATION   TESTS 


25 


curve,  and  from  these  observations  it  would  appear  as  if  the  rotation  of 
the  disk  somewhat  out  of  the  center  of  the  air-gap  caused  a  very  slightly 
larger  amount  of  heat  per  revolution.  The  general  form  of  the  curve 
shows  again  a  tendency  toward  a  maximum  heat  per  revolution  with  a 
speed  of  approximately  60  to  80  revolutions,  and  a  tendency  to  fall  off 
when  the  ergometer  is  running  at  a  high  speed. 

With  a  magnetizing  current  of  1.10  amperes,  we  have  two  series  of 
observations  that  are  by  no  means  concordant  (fig.  10),  and  yet  both 
indicate  a  noticeable  falling  off  in  the  heat  per  revolution  at  high  speed. 
We  are  unable  at  this  time  to  account  for  the  marked  discrepancy  be- 
tween these  two  sets  of  observations,  but  since  this  current  is  not  used 
at  present  in  actual  experimentation  with  man  and  since  the  curve  agrees 
with  the  others  in  its  general  form,  it  is  deemed  inadvisable  at  this  time 
to  repeat  the  calibration  test. 

The  calibrations  made  with  a  current  of  1.35  amperes  lie  for  the  most 
part  on  a  very  definite  curve  (fig.  11).  In  one  single  observation  at  80 
revolutions  per  minute,  it  is  approximately  5  per  cent  too  high.  The  gen- 
eral form  of  curve  noted  for  the  other  calibrations  is  here  markedly  shown, 
namely,  a  low  heat  per  revolution  with  a  low  speed,  a  fairly  constant 
heat  per  revolution  between  60  and  80  revolutions  per  minute,  and  then 
a  falling  off  in  the  heat  per  revolution  as  the  speed  is  increased. 


.021 
.020 

.019 
.01  8 
.01  7 
O1  6 

X 

A 

^ 

; 

*\ 

/ 

\ 

^x 

^s 

X 

5O       6O       7O       8O       9O       1OO      11O      12O 

Fia.  11. — Calibration  curve  of  ergometer  II  for  magnetizing  current  of  1.35  amperes. 

The  observations  with  the  strongest  current  through  the  field,  namely, 
1.50  amperes,  are  shown  in  fig.  12.  One  observation,  characterized  by  a 
circle,  was  made  when  the  disk  was  rotating  near  the  rear  pole,  i.e.,  out  of 
center  of  the  air-gap,  but  the  variation  from  the  normal  is  so  slight  as  to 
make  it  almost  imperceptible.  In  this  curve  we  again  find  a  low  heat 
per  revolution  with  low  speed,  a  fairly  constant  heat  per  revolution  be- 
tween 60  and  80  revolutions  per  minute,  and  a  decrease  in  the  heat  per 
revolution  as  the  speed  is  further  increased. 


26 


A    BICYCLE    ERGOMETER    WITH   AN    ELECTRIC    BRAKE 


By  far  the  largest  number  of  tests  were  made  with  a  current  of  1.25 
amperes,  which  was  selected  for  the  study  of  the  magnetic  field  described 
in  Part  III  of  the  report.  In  order  to  make  this  study  it  was  necessary 
to  move  the  disk  as  far  as  possible  toward  the  rear  pole-face  and  thus 
provide  space  in  the  air-gap  between  the  front  pole-face  and  the  disk  for 
a  flat  bismuth  spiral.  It  was  deemed  advisable,  therefore,  to  test  the 
machine  under  these  conditions  in  order  to  find  if  there  was  any  marked 
difference  in  the  calibration  test  when  the  circular  disk  was  somewhat 
off  center.  The  points  obtained  in  this  way  are  surrounded  by  circles 
in  the  curve  shown  in  fig.  13.  It  will  be  seen  that  they  lie  somewhat 
above  the  curve,  as  was  also  the  case  with  figs.  9  and  12.  The  reason 
doubtless  is  that  the  magnetic  field,  at  least  near  the  edges  of  the  poles, 
is  so  non-uniform  that  the  lines  of  induction  intercepted  by  the  disk  are 
somewhat  denser  when  the  latter  is  brought  close  to  one  pole-face. 


A«ft0 

.022 
.021 
.O2O 
.019 
.018 
.017 
.01  6 
.015 

^^-' 

—  —  •  —  „ 

/ 

r 

X 

\ 

/ 

X 

V 

/ 

N 

/ 

/ 

/ 

3O       4O       5O       6O       7O       8O       9O       1OO      11O 

FIG.  12. — Calibration  curve  of  ergometer  II  for  magnetizing  current  of  1.50  amperes. 

Tests  were  also  made  with  the  magnet  covering  more  of  the  copper 
disk,  i.e.,  pushed  in  about  2  cm.  toward  the  hub.  Accordingly,  in  fig.  13 
we  find  a  large  number  of  points  which  may  be  classified  under  several 
groupings.  In  the  series  of  observations  in  which  the  magnet  was  pushed 
farther  over  the  copper  disk,  one  might  expect  a  somewhat  smaller  brake- 
effect  upon  the  copper  disk;  as  a  matter  of  fact,  it  was  found  that  the 
curve  was  shifted  somewhat  to  the  left,  showing  abnormally  high  values 
of  heat  per  revolution  at  low  speeds.  These  points  are  indicated  by 
squares  (cf.  Part  III).  Since  the  chief  use  of  the  instrument,  however, 
is  for  a  regular  magnetizing  current  of  1.25  amperes,  with  the  disk  ex- 
actly in  the  center  of  the  air-gap  and  the  periphery  of  the  disk  tangen- 


CALIBRATION   TESTS 


27 


tial  to  the  upper  edge  of  the  pole-face  of  the  magnet,  it  seemed  undesirable 
to  make  further  calibrations  of  this  instrument  under  these  peculiar 
conditions,  which  were  necessitated  only  by  the  study  of  the  magnetic 
field.  We  have,  therefore,  chiefly  to  consider  the  observations  made  with 
the  disk  in  the  regular  position.  The  heavy  line1  plotted  curve  represents 
all  observations  with  the  disk  and  magnet  in  their  original  positions. 
Here  again  we  find  with  low  speeds  the  low  heat  per  revolution  a  fairly 
constant  heat  per  revolution  with  a  speed  between  60  to  90,  and  a  fall 
in  heat  per  revolution  as  the  speed  increases  beyond  this. 


.022 
.021 
.020 

.01 9 

.018 
.01 7 
.01 6 
.015 

.014 
.013 


2O       3O       4O       5O       6O       7O       SO       9O       1OO      11O      12O 

Fid.  13. — Calibration  curves  of  ergometer  II  for  magnetizing  current  of  1.25  amperes. 
Black  crosses:  Disk  in  normal  position  between  poles  of  magnet;  curve  in  heavy  line  is  based  upon  these. 
Circles :  Disk  close  to  rear  pole,  air-gap  on  other  side  widened. 
Squares:  Poles  moved  2  cm.  in  toward  center  of  disk. 
Curve  in  light  line  represents  values  of  &>(f>2  (see  p.  37). 

To  show  their  similarity  the  curves  corresponding  to  the  five  magnet- 
izing currents,  0.95,  1.10,  1.25,  1.35,  and  1.50  amperes  have  been  replot- 
ted  on  one  diagram  (see  fig.  14).  This  series  of  curves  is  strikingly  simi- 
lar to  those  found  with  ergometer  I  when  calibrated  in  June  and  July 
of  1911,  and  indicates  that  the  instruments  are  essentially  alike  in  their 
mechanical  and  electrical  features.  The  special  feature  to  be  noted  here 
is  that  the  curves  show  uniformly  a  low  heat  per  revolution  with  a  low 
speed,  nearly  constant  heat  per  revolution  between  approximately  60  to 
90  revolutions  per  minute,  and  a  rapidly  falling  heat  per  revolution  at 
high  speeds.  Since  practically  all  experiments  are  made  with  bicycle 
riders  at  speeds  between  60  to  80,  it  may  be  stated  again  that,  in  general, 

1  The  lighter  lined  curve  is  discussed  in  Part  III,  p.  37. 


28 


A    BICYCLE    ERGOMETER    WITH    AN    ELECTRIC    BRAKE 


the  heat  per  revolution  is  sufficiently  constant  between  these  limits,  irre- 
spective of  speed,  although  reference  should  be  made  to  the  calibration 
curves  if  the  speeds  are  below  60  or  above  80.  The  abnormal  appearance 
of  these  curves  led  to  much  speculation  as  to  the  cause.  In  Part  III  of 
this  report  it  will  be  shown  that  a  complete  explanation  of  the  observed 
effects  is  found  in  the  magnetic  reaction  of  the  eddy  currents  induced  in 
the  copper  disk. 


.02  3 
.022 
.021 
.O2O 
.019 
.018 
.017 
.016 
.015 
.014 
.013 
.012 
.011 

<** 

•»^, 

/ 

<.SO 

AMP. 

\ 

X 

/ 

^s 

/ 

/ 

<3S 

AMP. 

\ 

x 

// 

/ 

«^ 

AMP. 

\ 

X 

[X 

\ 

/ 

/ 

^ 

X 

\ 

X 

/ 

*uo 

AMP' 

\ 

X 

\ 

S, 

x£s 

•^ 
AMP. 

^x 

\ 

\ 

/ 

\ 

Sy 

\ 

V 

X 

X 

^^ 

\ 

30       40       50       60       70       8O       9O       1OO      11O      12O 
FIG.  14. — Calibration  curves  of  ergometer  II  for  magnetizing  currents  of  0.95  to  1.50  amperes. 

For  physiological  experimenting,  the  apparatus  is  most  satisfactory, 
since  the  constant  brake-effect  gives  a  constant  heat  production.  Although 
unfortunately  it  is  not  everywhere  possible  to  determine  the  absolute 
values  by  means  of  calibration  tests  inside  a  large  calorimetric  chamber, 
yet  it  may  be  that  by  driving  the  ergometer  with  an  electric  motor  of 
known  efficiency  and  measuring  the  input  of  electrical  power,  an  approxi- 
mate idea  can  be  obtained  of  the  actual  power  required  to  rotate  the 
pedals.  We  have  made  some  rough  tests  of  this  sort.  The  chief  diffi- 
culty lies  in  running  the  disk  at  a  sufficiently  low  speed  without  the 
various  losses  becoming  disproportionately  large. 

In  connection  with  these  observations  it  is  of  especial  interest  to  note 
that  ergometer  I  remained  essentially  constant  in  its  electrical  and  mechan- 
ical properties  over  a  period  of  some  8  years,  thus  showing  a  remarkable 


CALIBRATION   TESTS 


29 


constancy  in  the  apparatus.  We  feel  justified,  therefore,  in  heartily 
recommending  its  use  when  a  constant  amount  of  work  is  to  be  done  and 
uniformity  in  muscular  work  is  essential.  Furthermore,  the  amounts  of 
energy  computed  from  the  speed  of  the  magnetizing  current  are  accu- 
rate to  within  about  2  per  cent. 

FRICTION  TESTS  WITH  ERGOMETER  II. 

Although  it  was  doubtful  if  a  knowledge  of  the  heat  per  revolution 
due  to  friction  would  be  of  any  particular  value,  it  seemed  desirable  to 
make  measurements  of  the  friction  of  this  apparatus  if  only  for  com- 
parison with  those  made  with  ergometer  I,  and  for  checking  the  recent 
experiments  with  the  latter.  Three  friction  tests  were  accordingly  made 
with  ergometer  II  on  December  18,  20,  and  22,  1911,  the  results  being 
reported  in  table  6.  As  in  the  friction  tests  with  ergometer  I,  the  amounts 
of  heat  measured  were  so  very  small  that  but  little  reliance  can  be  placed 
upon  the  results  for  individual  periods;  and  it  is  not  surprising  that  we 
find  variations  of  50  per  cent  between  the  heat  per  revolution  found  on 
December  18  and  December  22  when  compared  with  that  in  the  test  on 
December  20.  When  we  consider,  for  example,  that  through  a  whole 
experiment  lasting  from  10h  14m  a.  m.  to  2h  15m  p.  m.  only  a  sum  total  of 
7  calories  was  measured,  the  numerical  values  found  are  certainly  not 
of  great  significance.  The  important  thing  is  that  these  results  show 
an  average  of  heat  per  revolution  not  far  from  0.0025  calorie,  which  is  in 
reasonably  close  agreement  with  those  found  with  ergometer  I  in  the 
calibrations  inside  of  this  identical  calorimeter.  In  general,  the  frictional 
heat  per  revolution  is  not  far,  therefore,  from  1  to  2  per  cent  of  the  total 
heat  produced  when  the  apparatus  is  used  with  the  field  magnetized  at 
1.5  amperes. 

TABLE  6. — Friction  test,  ergometer  II. 


Corr.  for 

Heat 

No.  of 

Rate  j      ueat 

Time. 

meas- 
ured. 

change 
of  cal. 

pro- 
duced. 

revolu- 
tions of 

P?r       per  revo- 
mm-        lution. 

temp. 

ute.    | 

CO/8. 

cals- 

cals. 

cal. 

1911  Dec.  18,  2K)2°>p.m.  to  5b02">p.m. 
Dec.  20,  10  14  a.m.  to  2  15  p.m. 
Dec.  22,  10  46  a.m.  to  4  46  p.m. 

12.4 
7.08 
14.89 

-4.5 
-1.6 
+  1.0 

7.9 

5.48 
15.89 

22,276 
30,121 
45,235 

124    0.000355 
125  ;  .000182 
126  I  .000351 

I 

PART  III. 


THE  MAGNETIC  REACTIONS  PRODUCED  BY  A  COPPER  DISK 
ROTATING  BETWEEN  THE  POLES  OF  A  MAGNET. 

That  a  rotating  disk  exerts  not  merely  a  tangential  drag,  but  also  a 
repulsive  force,  on  a  magnet  pole  placed  near  it,  has  been  known  since 
the  days  of  Arago.1  Nobili 2  first  discovered  that  the  loops  of  induced 
current  are  displaced  in  the  direction  of  rotation  of  the  disk,  though  he  did 
not  understand  the  part  played  by  self-induction  in  causing  this.  Indeed, 
as  far  as  we  are  aware,  no  attempt  has  been  made  up  to  the  present  time  to 
make  a  quantitative  determination  of  the  electric  and  magnetic  effects. 

Mathematically,  the  problem  of  the  currents  induced  in  bodies  rotating 
in  a  magnetic  field  has  been  attacked  by  Felici,  Jochmann,  Maxwell, 
Himstedt,  Niven,  Larmor,  Gans,  and  especially  by  Hertz.3  The  chief 
results  of  Hertz's  work  that  have  a  bearing  on  the  present  paper  may  be 
summarized  as  follows:  When  a  conducting  mass  is  rotated  in  a  mag- 
netic field,  the  induced  currents,  owing  to  self-induction,  are  distorted 
in  the  direction  of  rotation  to  an  extent  independent  of  the  intensity 
of  the  magnetic  field  but  increasing  with  the  angular  velocity.  At  the 
surface  of  the  conductor  the  currents  are  less  distorted  than  in  the  interior. 
At  infinite  angular  velocity  the  surface  of  the  conductor  would  act  toward 
magnetic  forces  like  a  conducting  surface  in  an  electric  field,  screening 
the  interior  entirely  from  all  magnetic  action. 

These  mathematical  investigations  were  all  made  on  the  assumption 
of  certain  ideal  conditions,  which  in  general  it  would  be  hard  to  realize 
experimentally.  In  order  to  apply  theoretical  principles  at  all  to  the 
present  case  it  is  necessary  to  make  some  simple  assumptions  and  to  be 
content  with  qualitative  relations.  The  problem  would  be  comparatively 
simple  if  the  disk  were  so  thin  that  it  could  be  regarded  as  a  current  sheet, 
if  the  magnetic  induction  B  were  uniform  in  the  space  between  the  poles, 
and  if  the  self-induction  of  the  disk  could  be  neglected.  Calling  a>  the 
angular  velocity  of  the  disk,4  we  would  then  have  for  the  induced  electro- 
motive force 

e  =  constant  X  m  B 

1  Arago,  Pogg.  Ann.,  1826,  7,  p.  590;  Pohl,  Pogg.  Ann.,  1826,  8,  p.  369. 

2  Nobili,  Pogg.  Ann.,  1833,  27,  p.  401.    A  very  full  account  of  the  classical  experi- 
ments on  rotating  disks  is  given  in  Wiedemann's  "Galvanismus  und  Elektromagnetis- 
mus,"  Braunschweig,  1874. 

s  Felici,  Annali  di  sci.  mat.  e  fis.,  1853,  p.  173;  Jochmann,  Pogg.  Ann.,  1864,  122,  p. 
214;  Maxwell,  "Electricity  and  Magnetism,"  2,  p.  300;  Himstedt,  Wied.  Ann.,  1880, 
11,  p.  812;  Niven,  Proc.  Roy.  Soc.  30,  1880,  p.  113;  Larmor,  Phil.  Mag.  (5),  1884,  17, 
p.  1;  Gans,  Zschr.  f.  Math.  u.  Phys.,  1902,  48,  p.  1;  Hertz,  Inaugural  Dissertation,  also 
"Gesammelte  Werke,"  1,  1895,  p.  37. 

4In  Parts  I  and  II  speeds  were  expressed  in  revolutions  per  minute  of  the  pedals, 
because  in  using  the  bicycle  ergometer  this  is  the  important  quantity.  Since  in  Part 
III  attention  is  centered  chiefly  on  the  disk,  we  shall,  in  what  follows,  in  general  refer 
to  the  angular  velocity  or  number  of  revolutions  per  minute  of  the  disk,  obtained  by 
multiplying  all  pedal  speeds  by  3.25,  the  ratio  of  the  two  sprocket-wheels. 

31 


32  A   BICYCLE    ERGOMETER   WITH   AN    ELECTRIC    BRAKE 

Hence  the  currents  in  the  disk  would  be  proportional  to 

a>B 

(T 

where  o-  is  the  specific  resistance  of  the  disk.     The  rate  of  production  of 
heat  would  then  be  proportional  to 


<T 

and  the  heat  per  revolution  proportional  to 


Hence  if  these  most  elementary  assumptions  were  sufficient,  as  might 
easily  be  supposed  to  be  the  case,  the  heat  per  revolution  would  be  a  linear 
function  of  the  speed  instead  of  reaching  a  maximum  and  then  decreasing. 

In  the  actual  case  the  disk  is  of  finite  thickness  and  the  current  paths 
possess  a  self-inductance  depending  on  the  form  of  the  paths  and  on  the 
magnetic  constants  of  the  iron  pole-pieces.  Hence  the  current  density 
is  not  uniform  through  the  thickness  of  the  disk,  and  the  magnetic  field 
is  distorted  and  modified  by  the  reaction  of  the  eddy  currents  and  by  the 
changes  in  permeability,  to  an  extent  that  it  is  not  easy  to  predict. 

Nevertheless,  by  making  the  following  three  fundamental  assumptions, 
it  is  possible  to  establish  relations  between  speed,  resultant  magnetic 
induction,  and  rate  of  production  of  heat,  which  are  capable  of  experi- 
mental verification.  These  three  assumptions  are  obviously  valid  only 
at  low  speeds;  still,  our  observations  were  not  extensive  enough  to  fur- 
nish more  than  a  rough  test  for  the  theory. 

Owing  to  self-induction  the  currents  are  not  symmetrically  situated 
with  respect  to  the  magnet  poles,  but  are  advanced  in  the  direction  of 
rotation  of  the  disk  through  a  certain  angle  which  we  will  call  6.  In 
accordance  with  Hertz's  results  we  may  assume  that  for  moderate  speeds 

0  =  kl(o  (1) 

where  w  is  the  angular  velocity  of  the  disk  and  kl  a  constant  independent 
of  the  strength  of  the  magnetic  field.  This  condition  is  shown  in  fig.  16, 
page  40,  in  which  the  disk  is  supposed  to  rotate  counter-clockwise,  and 
the  magnetic  induction  to  be  directed  from  the  observer  into  the  disk. 
It  is  evident  that  the  system  of  current  loops  whose  magnetic  field  is 
opposed  to  the  field  of  the  electro-magnet  is  now  brought  more  nearly  be- 
tween the  magnet  poles.  If  there  were  no  such  displacement  of  the  loops, 
the  magnetic  induction  would  be  weakened  on  the  side  where  the  current 
paths  enter  the  air-gap,  and  strengthened  on  the  other  side.  This  would 
result  in  a  crowding  of  the  lines  away  from  the  "leading"  edge  of  the  pole, 
toward  the  "trailing"  edge.  The  resulting  decrease  in  permeability  on 
the  trailing  half  would  be  expected  of  itself  to  diminish  the  total  magnetic 
flux  somewhat.  But  owing  to  the  self-inductance,  the  field  must  be 
weakened  on  one  side  much  more  than  it  is  strengthened  on  the  other. 


MAGNETIC   REACTIONS  33 

The  total  original  flux  <f>0  across  the  disk  will  thus  be  diminished  by  a 
certain  amount  which  we  will  call  </>',  the  "counter  flux"  due  to  the  eddy 
currents.  This  diminution  in  flux  may  be  assumed  for  moderate  speeds  to 
be  proportional  to  the  intensity  i  of  the  eddy  currents  and  to  the  angle  0,  or 

*'  =  M*  (2) 

Thirdly,  in  accordance  with  the  fundamental  principle  of  electro- 
magnetic induction,  we  have 


where  the  actual  resultant  magnetic  induction  through  the  disk  is 


From  these  assumptions  (1),  (2),  and  (3),  the  following  equations 
may  be  derived,  in  which  the  product  kjc2k3  is  replaced  by  a  single  con- 
stant k  : 


As  will  be  seen,  these  assumptions  do  not  take  into  account  all  of  the 
variables;  nevertheless,  it  will  be  shown  on  p.  37  that  equation  (4) 
is  roughly  verified.  The  significance  of  equation  (5),  which  represents 
the  heat  per  revolution  of  the  disk,  will  be  discussed  in  a  later  paragraph. 

MEASUREMENT  OF  MAGNETIC  FIELD  BY  MEANS  OF  A 
BISMUTH  SPIRAL. 

It  seemed  desirable  to  measure  not  simply  the  total  magnetic  flux 
at  different  speeds,  but  the  induction  at  a  number  of  points  in  and  near 
the  air-gap  as  well.  Among  the  various  practicable  methods,  that  of 
the  bismuth  spiral  seemed  best  adapted  for  our  purpose.  Most  of  the 
observations  described  below  were  made  with  a  Hartmann  and  Braun 
spiral,  kindly  loaned  us  by  the  Worcester  Polytechnic  Institute.  The 
fine  bismuth  wire  of  this  spiral,  coiled  into  a  flat  disk  about  17  mm.  in 
diameter,  had  a  resistance  under  normal  conditions  of  about  20  ohms.  A 
small  portion  of  the  work  was  done  with  a  second  spiral,  similar  to  the 
first,  and  the  results  obtained  with  the  two  instruments  agreed  very  well. 
Unfortunately  we  did  not  have  at  our  disposal  a  spiral  of  smaller  diameter. 

In  order  to  make  it  possible  to  introduce  the  bismuth  spiral  into  the 
narrow  gap  between  pole-face  and  disk,  it  was  necessary  to  shift  the  electro- 
magnet slightly,  bringing  one  of  its  faces  almost  into  contact  with  the  disk, 
while  the  gap  on  the  other  side  was  correspondingly  widened.  The  effect 
of  this  change  on  the  heat  per  revolution  was  considered  in  Part  II.  Even 
with  this  increased  air-space  on  one  side  of  the  disk,  it  was  not  easy  to 
bring  the  spiral  into  the  center  of  the  field  without  its  being  chafed  by  the 


34  A    BICYCLE    ERGOMETER   WITH   AN    ELECTRIC    BRAKE 

disk.  Hence  but  few  observations  were  made  in  the  center  of  the  field, 
and  no  reliable  ones  were  obtained  there  when  the  disk  was  rotating. 
During  the  magnetic  observations  the  ergometer  was  mounted  inside  the 
calorimeter,  but  the  front  of  the  calorimeter  was  open  and  no  attempt  was 
made  to  allow  the  thermal  conditions  to  reach  a  steady  state;  each  speed 
was  generally  maintained  for  only  a  minute  or  less.  Hence  in  general  the 
temperature  of  the  disk  was  somewhat  lower  than  during  the  calibra- 
tion tests. 

The  bismuth  spiral  was  clamped  securely  in  a  holder  that  was  capable 
of  being  moved  parallel  to  itself  in  various  directions.  In  nearly  all 
cases  the  exciting  current  in  the  electro-magnet  was  1.25  amperes  and  in 
the  few  remaining  cases  the  results  have  been  corrected  to  this  value. 
Resistances  were  measured  with  a  Wolff  Wheatstone  bridge  and  sensitive 
galvanometer. 

The  spiral  received  heat  by  radiation  from  the  copper,  and  by  con- 
duction from  the  strong  current  of  air  when  the  disk  was  in  motion.  As 
this  made  a  direct  determination  of  its  temperature  impossible,  it  was 
decided  to  estimate  the  temperature  from  the  resistance  of  the  bismuth 
when  the  magnetic  field  was  off.  This  resistance  was  measured  at  fre- 
quent intervals  and  the  temperature  computed  with  the  aid  of  the  resist- 
ance temperature  coefficient  of  bismuth.  Thus,  in  a  typical  group  of 
observations  at  each  position  of  the  spiral,  the  following  resistances  were 
observed:  (1)  magnetic  field  off,  disk  stationary;  (2)  magnetic  field  on, 
disk  stationary;  (3)  field  on,  disk  running  at  two  or  more  speeds  in  suc- 
cession, in  many  cases  repeating  in  reverse  order;  (4)  field  still  on,  disk 
stationary;  (5)  field  off ,  disk  stationary. 

Allowance  was  made  whenever  necessary  for  the  drift  in  temperature 
between  observations  (1)  and  (5).  In  general,  the  mean  of  (1)  and  (5) 
gave  iv0,  the  resistance  of  the  spiral  in  a  magnetic  field  of  intensity 
(practically)  zero.  The  remaining  observations  gave  values  of  wf,  the 
resistance  with  field  on,  at  various  speeds.  In  most  cases  the  speeds  were 
0,  11,  60,  and  112  revolutions  per  minute  of  the  pedals,  or  0,  36,  195,  and 
364  revolutions  per  minute  of  the  disk.  For  each  speed  the  value  of 
ivf—w0  was  corrected  for  temperature,  and  from  this  the  induction  in 
gausses  was  obtained  from  the  calibration  curve  furnished  with  the  spiral. 
At  the  conclusion  of  each  set  of  observations  the  spiral  was  advanced 
a  millimeter  or  so  and  the  observations  repeated. 

Most  of  the  magnetic  distortion  was  to  be  looked  for  along  lines  paral- 
lel to  the  direction  in  which  the  portion  of  the  disk  between  the  poles  was 
moving,  i.e.,  along  the  line  AB  in  fig.  16.  Nearly  all  of  the  observations 
were  accordingly  made  along  this  line  and  they  will  be  considered  first. 
The  results  are  shown  in  fig.  15,  in  which  the  abscissae  represent  dis- 
tances in  millimeters  measured  from  the  center  of  the  field  along  the  line 
AB  of  fig.  16.  Positive  values  lie  in  the  direction  in  which  the  disk  is 
supposed  to  be  rotating.  The  heavy  vertical  lines  G  G'  in  fig.  15  indi- 


MAGNETIC    KEACTIONS 


35 


cate  the  position  of  the  edges  of  the  magnet  pole;  thus  G'  is  the  "trailing 
tip."  The  curves  in  heavy  lines  show  the  observed  induction  in  gausses 
at  different  angular  velocities.  The  number  of  revolutions  per  minute 
of  the  disk  is  indicated  on  each  curve.  To  avoid  confusion,  the  individual 
observations  are  omitted,  except  in  the  case  of  one  curve.  The  points  for 


-40mm     -20 


40mm 


FIG.  15. — Magnetic  induction  across  air-gap.     Direction  of  motion  of  disk  is  to  right. 
G,  G'  indicate  position  of  edges  of  magnet  poles. 


36  A   BICYCLE    EEGOMETER   WITH   AN    ELECTRIC    BRAKE 

the  other  curves  agree  among  themselves  to  about  the  same  degree  of 
closeness  as  these.  Owing  to  the  unsatisfactory  character  of  the  obser- 
vations in  the  middle  of  the  field  when  the  disk  was  in  motion,  but  little 
weight  was  placed  on  these  data,  and  the  curves  are  accordingly  shown 
as  broken  lines  in  this  region. 

Since  the  bismuth  wire  was  coiled  in  a  spiral  about  17  mm.  in  diameter, 
it  is  clear  that  these  curves  can  not  show  accurately  the  precise  form  of 
the  magnetic  field.  A  simple  consideration  shows  that  if  the  curves 
could  be  drawn  with  precision  they  would  slope  more  steeply  than  the 
curves  here  drawn;  they  would  then  cross  the  lines  G  G'  at  points  higher 
up,  and  the  maxima  would  all  be  higher.  Still,  crude  as  they  are,  they 
show  clearly  the  reaction  of  the  eddy  currents  in  the  disk. 

The  curve  obtained  with  the  disk  stationary  (speed  0),  is  quite  sym- 
metrical, showing  slight  maxima  close  to  the  edges  of  the  poles.  As 
the  speed  increases,  the  distortion  of  the  magnetic  field  and  the  marked 
decrease  in  flux  at  high  speeds  are  very  evident.  From  the  curve  for 
speed  364,  it  might  be  inferred  that  here  the  induced  current  is  confined 
entirely  to  a  narrow  path  close  to  the  trailing  edge  of  the  pole-face.  That 
this  is  the  case  will  be  shown  later. 

Since  the  ordinates  of  the  curves  for  speeds  36,  195,  and  364  represent 
the  resultant  induction  through  the  disk,  it  is  evident  that  the  algebraic 
difference  between  these  ordinates  and  those  for  speed  0  must  be  a 
measure  of  the  magnetic  field  that  would  be  produced  by  the  induced 
currents  alone.  These  differences  are  plotted  in  fine  lines.  Negative 
ordinates  signify  a  component  opposing  the  flux  from  the  electro-magnet. 
The  most  striking  feature  of  these  curves  is  the  very  pronounced  demag- 
netizing field  produced  in  the  disk  at  high  speeds.  The  points  where  the 
curves  cross  the  axis  of  abscissae  show  that  the  displacement  of  the  cur- 
rents in  the  direction  of  rotation  increases  with  the  speed  (eq.  (1)),  though 
at  a  lower  rate.  It  is  presumably  near  these  points  that  the  induced 
currents  attain  their  maximum  values. 

A  few  observations  were  made  with  the  bismuth  spiral  in  other  posi- 
tions. The  induction  was  found  to  be  practically  uniform  when  the 
spiral  was  moved  in  a  radial  direction,  except  close  to  the  outermost  edge 
of  the  magnetic  field  near  the  circumference  of  the  disk,  for  example  at 
the  point  P  in  fig.  16.  Here  the  flux  density  was  found  to  increase  with 
increasing  speed,  as  would  be  expected,  for  the  demagnetizing  effect  of 
the  currents  must  lead  partly  to  a  diminution  in  the  total  flux  around  the 
magnetic  circuit,  and  partly  to  increased  leakage  around  the  outer  edge 
of  the  disk.  Indeed,  the  currents  along  the  edge  of  the  disk  on  the 
side  approaching  the  magnet  flow  in  such  a  direction  as  to  bend  the  lines 
of  magnetic  induction  outward  around  the  edge  of  the  disk. 

When  the  spiral  was  laid  flat  against  the  side  of  the  magnet  pole, 
with  its  plane  perpendicular  to  the  disk,  it  showed  a  decrease  of  about 
30  per  cent  in  magnetic  induction  on  the  "leading"  side,  while  on  the 


MAGNETIC    REACTIONS 


37 


"trailing"  side  the  induction  was  about  doubled  when  the  disk  was  run- 
ning at  364  revolutions  per  minute. 

COMPARISON  OF  RESULTS  WITH  THEORY. 

Although,  for  the  reasons  given,  the  curves  in  fig.  15  do  not  represent 
the  facts  quite  accurately,  still  it  is  worth  while  to  inquire  how  well  they 
satisfy  the  conditions  expressed  in  equations  (4)  and  (5).  In  these  equa- 
tions it  is  necessary  to  know  the  value  of  <f>,  the  resultant  flux  at  angular 
velocity  w,  and  9',  the  "counter  flux"  at  the  same  angular  velocity. 
From  the  areas  of  the  distorted  curves  in  heavy  lines  9  is  obtained,  and 
9'  from  the  areas  of  the  curves  in  fine  lines  (algebraic  sum  of  negative 
and  positive  lobes).  The  areas  were  taken  arbitrarily  between  — 40  and 
+45  mm.,  since  outside  of  these  limits  the  ordinates  are  small.  From 
the  areas  and  the  measured  dimensions  of  the  pole-faces,  the  values 
shown  in  columns  2  and  3  of  table  7  were  obtained. 

TABLE  7. — Magnetic  fluxes  at  different  speeds. 


ft) 

4> 

If 

ft>2T>X  !0"3 
9 

ft>p2  X  10~9 

36 

65,000 

800 

105 

152 

195 
364 

42,200 
27,700 

23,600 
38,100 

68 
96 

348 
279 

Since  only  relative  values  are  required,  <o  is  here  given  as  the  num- 
ber of  revolutions  per  minute  of  the  disk. 


The  quantity  o>2^>  in  column  4  should,  by  equation    (4),  be  equal 
to  j-,  a  constant.     This  condition  is  satisfied  as  well  as  could  be  ex- 

pected, considering  that  the  increase  in  a  from  the  first  to  the  third  ob- 
servation is  ten-fold  and  the  increase  in  9'  is  nearly  fifty-fold.  It  must 
also  be  remembered  that  as  the  speed  increases,  the  distribution  of  the 
current  paths  and  hence  also  the  resistance  of  the  paths  may  change  to 
a  marked  degree.  In  other  words,  our  assumptions  considered  only  the 
total  flux,  although  theoretically  the  distribution  of  magnetic  induction 
and  of  the  current  loops  in  space  ought  to  be  considered.  Moreover, 
since  the  magnetic  lines  pass  between  pole-pieces  of  limited  extent,  it  is 
possible  that  our  first  assumption,  equation  (1),  does  not  hold  at  the 
higher  speeds.  Changes  of  a-  with  temperature  can  hardly  have  affected 
the  result  materially;  but,  on  the  other  hand,  the  lack  of  reliable  obser- 
vations in  the  central  portions  of  the  field  lends  an  element  of  uncertainty. 
In  equation  (5)  we  expressed  the  relation 


209177 


38  A   BICYCLE    ERGOMETER    WITH   AN   ELECTRIC    BRAKE 

The  left-hand  member  of  this  equation  is  proportional  to  the  heat 
generated  per  revolution  of  the  disk,  since  the  numerator  represents  the 
rate  of  production  of  heat,  while  the  denominator  indicates  the  number 
of  revolutions  per  minute.  We  are  thus  in  a  position  to  obtain  relative 
values  for  the  heat  per  revolution,  based  on  magnetic  data  alone,  which 
can  be  compared,  for  the  same  current  in  the  electro-magnet  (1.25  am- 
peres), with  the  calibration  curve  of  the  ergometer  (fig.  13).  Since  k3 
is  a  constant  and  the  temperature  of  the  disk  changed  but  little  during 
the  magnetic  tests,  it  is  sufficient  to  compute  the  values  of  cocf>2  at  various 
speeds  and  to  plot  these  values  as  functions  of  the  speed.  The  values  of 
o>$2  corresponding  to  the  three  observed  values  of  <f>  are  given  in  table  7. 

In  order  to  draw  the  entire  curve,  it  was  necessary  first  to  find  the 
relation  between  </>  and  co.  This  relation,  which  can  be  derived  from  our 
fundamental  assumptions,  is 


where  a  and  6  are  constants.  The  equation  is  roughly  satisfied  by  our 
observed  values  of  </>  and  o>,  but  we  considered  it  better  to  obtain  values 
of  <£  corresponding  to  various  values  of  co  from  a  curve  connecting  these 
quantities.  Since  the  curve  was  nearly  a  straight  line  over  the  observed 
range,  the  interpolation  was  simple.  To  facilitate  the  comparison  with 
the  ergometer  calibration  curve  for  1.25  amperes,  all  of  the  values  of  <w$2 
were  multiplied  by  a  constant  numerical  factor,  so  that  the  maximum 
of  the  calibration  curve  coincided  with  one  point  of  the  <w$2  curve.  In 
fig.  13  the  o>4>2  curve  is  shown  as  a  fine  line.  It  has  the  same  general 
form  as  the  calibration  curve,  but  its  maximum  comes  at  a  lower 
speed.  This  is  no  doubt  due  in  large  measure  to  the  sources  of  error 
already  mentioned.  But  it  may  also  be  due  partly  to  the  fact  that  since 
no  attempt  was  made  in  the  magnetic  tests  to  reach  thermal  equilibrium, 
the  copper  disk  was,  for  the  same  speed,  cooler  during  the  magnetic  tests 
than  during  the  calibrations.  At  low  speeds,  where  <f>  is  nearly  constant, 
the  relatively  small  value  of  a-  during  the  magnetic  tests  would  make  the 
heat  per  revolution  relatively  high.  But  at  high  speeds  a  smaller  value 
of  <r  means  a  larger  value  of  <£',  hence  a  relatively  small  value  of  </>. 
Since  equation  (5)  shows  that  the  heat  per  revolution  varies  as  the  square 
of  <£,  the  result  will  be  a  relatively  small  value  of  o>c/>2.  A  rough  calcu- 
lation shows  that  the  correction  from  this  cause  would  amount  perhaps 
to  5  per  cent,  raising  the  ordinates  to  the  right  of  the  maximum  of  the 
&></>2  curve  slightly,  and  reducing  those  to  the  left. 

Nevertheless,  aside  from  minor  discrepancies,  the  similarity  of  the 
two  curves  is  very  striking,  proving  beyond  a  reasonable  doubt  that  the 
peculiarity  in  the  ergometer  calibrations  is  due  almost  entirely  to  the 
demagnetizing  effect  of  the  eddy  currents  in  the  disk.  The  increased 
temperature  of  the  disk  at  high  speeds,  by  reducing  the  intensity  of  the 
currents,  enhances  this  peculiarity,  but  only  to  a  minor  degree. 


MAGNETIC   REACTIONS  39 

FURTHER  EXPERIMENTS  WITH  THE  EDDY  CURRENTS. 
The  great  intensity  of  the  currents  in  the  disk  was  also  made  evident 
by  the  following  quite  elementary  experiments: 

(I)  Compass  tests.— A  small    pocket  compass  held  near  the  disk 
showed  the  presence  of  a  strong  magnetic  field  due  to  the  eddy  currents, 
even  at  a  considerable  distance  from  the  electro-magnet.     One  way  of 
testing  this  was  to  trace  out  the  magnetic  lines  parallel  to  the  surface 
of  the  disk  by  the  usual  step-by-step  method,  holding  the  compass  with 
its  plane  vertical  like  a  dip  needle,  close  to  the  disk  near  one  pole  of  the 
magnet,  and  then  advancing  it  by  stages  parallel  to  the  disk  and  along 
the  direction  of  the  lines.     In  fig.  16  the  heavy  lines  marked  0  were  thus 
obtained  with  the  disk  stationary,  showing  the  direction  of  the  stray  lines 
from  the  electro-magnet.1     The  dotted  lines  marked  390  were  obtained 
when  the  disk  rotated  at  390  revolutions  per  minute.     In  this  figure  the 
north  pole  of  the  electro-magnet  is  on  the  side  toward  the  observer  and 
the  disk  rotates  counter-clockwise.     Observations  at  points  on  the  other 
side  of  the  magnet  pole  showed  a  corresponding  change  in  the  direction 
of  the  resultant  magnetic  field  when  the  disk  was  in  rotation.     The  point 
Q,  just  outside  the  disk,  is  a  neutral  point,  where  the  field  due  to  the  eddy 
currents  is  equal  and  opposite  to  that  due  to  the  magnet. 

(II)  Galvanometer  tests. — The  copper   leads    from  a  sensitive  gal- 
vanometer were  touched  to  the  surface  of  the  disk  at  points  from  1  to  5 
mm.  apart,  the  points  being  so  oriented  that  the  galvanometer  showed 
no  deflection.     Care  was  taken  to  reduce  the  effect  of  thermo-electric 
forces  to  a  minimum.     This  is  the  old  method  used  by  Faraday  and  Nobili 
for  plotting  the  lines  of  current  flow.     Though  it  can  not  always  be  as- 
sumed that  the  current  flows  in  a  direction  perpendicular  to  the  line 
joining  these  "equipotential"  points,  still  they  furnish  an  approximate 
idea  of  the  direction  taken  by  the  current  paths.     A  few  such  pairs  of 
points  are  indicated  in  fig.  16,  and  with  their  aid  some  of  the  current  lines 
have  been  constructed,  the  arrow-heads  indicating  the  direction  of  flow. 
These  lines  must  not  be  confused  with  the  magnetic  lines  described  above. 
Tests  made  close  to  the  magnet  pole  proved  that  at  390  revolutions  per 
minute  the  inwardly  directed  current  lines  were  confined  to  a  narrow 
band  about  a  centimeter  wide,  near  the  trailing  edge  of  the  pole,  as  shown. 
The  demagnetizing  effect  of  the  currents  is  here  very  evident. 

(III)  Intensity  of  the  eddy  currents. — The  galvanometer  leads  were 
touched  to  the  disk,  as  described  above,  at  a  point  near  the  magnet  pole, 
but  oriented  in  such  a  way  as  to  produce  a  maximum  deflection.     From 
the  distance  between  the  points  of  contact  and  the  resistance  and  sen- 
sitiveness of  the  galvanometer,  the   potential  difference  between  the 
points  was  found,  and  from  this  and  the  specific  resistance  of  copper 

1  At  the  time  of  these  tests  the  magnetic  poles  were  pushed  in  about  2  cm.  from  the 
outer  edge  of  the  disk.  This  can  hardly  have  produced  an  appreciable  change  in  any 
of  the  quantities  observed  (cf.  fig.  13). 


40  A    BICYCLE    ERGOMETER   WITH    AN    ELECTRIC    BRAKE 

the  current  density  was  found  to  be  of  the  order  of  650  amp. /cm2.    This 
was  at  about  300  revolutions  per  minute  of  the  disk. 

As  a  rough  check  on  this,  the  electromotive  force  induced  in  the  copper 
was  computed  from  the  observed  flux  and  the  speed  of  the  disk.  The 
potential  gradient  was  found  to  be  of  the  same  order  of  magnitude  as 


FIG.  16. — Magnetic  lines  and  current  loops  on  surface  of  rotating  disk.     Long 
arrow  shows  direction  of  rotation. 

that  derived  from  the  galvanometer  observations  above,  namely,  about 
one-thousandth  of  a  volt  per  centimeter.  From  these  data  we  estimate 
the  total  current  in  the  disk  to  have  been  not  less  than  2000  amperes. 
(IV)  Effect  of  eddy  currents  on  the  flux  through  the  magnet  coils. — 
In  order  to  measure  the  diminution  in  total  flux  when  the  disk  was 


MAGNETIC    REACTIONS  41 

running,  a  single  turn  of  wire  was  wrapped  around  one  of  the  magnet  coils 
and  connected  to  a  ballistic  galvanometer.  The  throw  was  measured 
when  the  field  current  was  turned  on,  and  again  when  the  disk  was  sud- 
denly set  in  rotation.  The  latter  throw  was  always  in  the  opposite  direc- 
tion to  the  former;  its  measured  value  was  certainly  somewhat  too  small, 
since  it  took  an  appreciable  time  for  the  disk  to  attain  full  speed.  The 
results  indicated  a  diminution  of  the  total  flux  amounting  to  only  about 
4  per  cent,  when  the  disk  rotated  at  320  revolutions  per  minute.  Even 
allowing  for  the  gradual  acceleration  of  the  disk,  it  is  apparent  that  the 
reaction  of  the  eddy  currents  causes  chiefly  an  increased  magnetic  leak- 
age, without  greatly  diminishing  the  flux  through  the  coils. 

The  diminution  of  the  flux  on  starting  the  disk  causes  a  slight  momen- 
tary increase  in  the  current  through  the  electro-magnet,  while  suddenly 
stopping  the  disk  diminishes  the  magnetizing  current  for  an  instant. 
This  is  analogous  to  the  momentary  changes  produced  in  the  current 
through  a  coil  of  wire  when  an  iron  core  is  moved  in  and  out.  Soret1 
seems  to  have  observed  this  effect  first.  On  the  other  hand,  Jacobi2 
asserted  that  the  magnetizing  current  was  diminished  when  the  angular 
velocity  of  his  disk  was  increased.  If  we  understand  his  paper  aright, 
this  must  have  been  an  error. 

(V)  Effect  of  eddy  currents  on  permanent  magnets. — It  is  of  interest 
to  consider  briefly  the  effect  of  moving  masses  of  metal  on  permanent 
magnets.  If  the  pole  of  a  bar  magnet  is  held  close  to  a  rapidly  revolv- 
ing copper  disk,  its  moment  is  permanently  weakened.  This  method  is 
sometimes  made  use  of  in  the  artificial  seasoning  of  horseshoe  magnets. 
In  the  design  of  at  least  one  type  of  speedometer,  this  demagnetizing 
action  is  especially  guarded  against  in  an  ingenious  manner. 

If  one  of  the  magnet  systems  of  a  Kelvin  galvanometer  employing 
astatic  needles  is  inclosed  in  a  copper  damper,  this  system  undergoes  a 
slight  demagnetizing  action  at  every  swing.  Thus  in  time  the  astaticism 
of  the  systems  must  be  perceptibly  impaired,  unless  the  needles  are  very 
well  hardened. 

The  currents  induced  in  masses  of  metal  moving  relatively  to  per- 
manent magnets  must,  at  the  beginning  and  end  of  the  motion,  induce 
eddy  currents  in  the  magnet  itself.  If  the  acceleration  is  the  same  on 
starting  and  stopping,  these  currents  can  have  little  to  do  with  the  demag- 
netization of  the  magnet,  for  they  flow  in  a  direction  tending  to  increase 
the  magnetization  when  the  motion  begins,  and  tending  to  decrease  it 
when  the  motion  ceases.  The  case  is  analogous  to  moving  the  keeper 
of  a  horseshoe  magnet  rapidly  up  against  the  poles,  which  causes  de- 
magnetizing eddy  currents  to  flow,  while  suddenly  pulling  off  the  keeper 
gives  rise  to  currents  in  the  opposite  direction. 

1  Soret,  Comptes  rendus,  1857, 45,  p.  301 .          2  Jacobi,  Comptes  rendus,  1873,  74,  p.  237. 


42  A  BICYCLE    ERGOMETER   WITH    AN   ELECTRIC    BRAKE 

INFLUENCE  OF  TEMPERATURE  ON  THE   CONSTANCY 
OF  THE  BICYCLE  ERGOMETER. 

From  what  has  preceded,  it  is  clear  that  the  rate  of  heat  production 
varies  inversely  as  the  resistance  of  the  rotating  disk,  and  hence  that 
the  heat  per  revolution  varies  in  the  same  manner.  Over  the  usual  range 
of  room  temperatures,  it  may  be  assumed  that  the  same  expenditure  of 
energy  in  the  disk  raises  its  temperature  to  the  same  extent  above  its 
surroundings.  If  the  ergometer  is  used  outside  the  calorimeter  in  a  room 
at  the  same  temperature  as  that  inside  the  calorimeter  during  calibration, 
the  results  of  the  calibrations  can  be  applied  without  correction,  provided 
the  circulation  of  air  is  approximately  the  same  in  the  two  cases.  But  if, 
for  example,  an  accuracy  of  2  per  cent  in  the  energy  measured  is  desired, 
then,  since  the  temperature  coefficient  of  copper  is  approximately  0.004, 
a  temperature  correction  will  have  to  be  applied  if  the  temperature  of  the 
room  differs  by  more  than  5°  C.  from  the  mean  temperature  inside  the 
calorimeter  during  calibration.  In  general,  during  the  work  that  has 
been  done  thus  far  with  the  ergometer,  no  such  correction  has  been  neces- 
sary. The  highest  observed  temperature  of  the  disk  (see  Part  II)  was 
43°  C.  at  a  pedal  speed  of  1  20  revolutions  per  minute,  the  room  tempera- 
ture being  20°  C.  It  was  to  be  expected  that  as  the  speed  increased  the 
maximum  temperature  would  occur  at  a  higher  speed  than  the  maximum 
value  of  the  heat  per  revolution,  since  the  maximum  temperature  depends 
on  the  heat  per  second,  i.e.,  it  is  proportional  to  the  heat  per  revolution 
multiplied  by  the  speed.  In  using  the  ergometer  for  accurate  quantita- 
tive measurements,  care  should  always  be  taken  to  maintain  each  speed 
long  enough  for  the  temperature  of  the  copper  disk  to  reach  a  sufficiently 
steady  state.  For  practical  purposes,  this  precaution  is  seldom  necessary. 

THE  DESIGN  OF  ELECTRIC  BRAKES. 

In  conclusion,  we  will  summarize  briefly  the  general  principles  that 
ought  to  be  considered  in  the  design  of  apparatus  employing  electro- 
magnetic damping,  particularly  with  reference  to  the  demagnetizing 
effects  of  the  eddy  currents.  We  shall  base  our  deductions  in  part  on  the 
equation 

(6) 


derived  from  our  fundamental  assumptions  on  p.  32.  </>„  is  the  impressed 
flux  when  the  disk  is  stationary,  <w  the  angular  velocity,  a-  the  specific 
resistance,  and  k  a  constant. 

(a)  Material  of  disk.  —  For  the  strongest  effects  soft  iron  or  soft  steel 
may  be  used.  The  resistance  is  of  course  comparatively  high,  but  the 
magnetic  induction  will  be  very  large,  and  the  heating  due  to  hysteresis 
will  be  added  to  that  from  the  eddy  currents.  The  magnetic  reaction 
from  an  iron  disk  must  be  very  large,  as  was  indeed  shown  by  Hertz  in 
the  paper  already  cited.  Copper  and  aluminum  are  probably  the  most 


MAGNETIC    REACTIONS  43 

widely  used  metals  on  account  of  their  low  specific  resistance.  Aluminum 
has  also  a  high  specific  heat  to  recommend  it.  If  a  weaker  effect  is  de- 
sired, an  alloy  of  high  resistance  may  be  used.  Other  things  being  equal, 
the  demagnetizing  effect  of  the  eddy  currents  will  be  greatest  for  an  iron 
disk,  with  copper  and  the  other  non-magnetic  metals  following  in  the 
order  of  their  specific  resistances.  But  for  the  same  expenditure  of  power 
the  demagnetizing  effect  will  be  practically  independent  of  the  material 
of  the  disk. 

(6)  Thickness  of  disk. — With  the  same  magnetic  flux,  the  intensity  of 
the  induced  currents  and  also  the  heat  will  vary  directly  as  the  thickness. 
Since,  according  to  Hertz,  the  currents  in  the  interior  of  a  thick  disk  lag 
more  than  those  on  the  surface,  it  follows  from  equation  (2)  that  the 
demagnetizing  effect  will  increase  at  a  more  rapid  rate  than  will  the  thick- 
ness of  the  disk. 

In  conjunction  with  the  magnetic  field  and  gear  ratio  employed,  the 
particular  thickness  of  disk  used  in  these  ergometers  fortunately  was  just 
such  as  to  produce  a  nearly  constant  heat  per  revolution  over  the  range 
of  speeds  commonly  used  by  riders. 

(c)  Diameter  of  disk. — This  is  probably  of  small  consequence  as  long 
as  the  magnet  pole  covers  only  a  small  part  of  the  surface  of  the  disk. 
The  essential  factor  is  the  linear  velocity  of  the  metal  under  the  pole. 

(d)  Linear  velocity. — The  expenditure  of  power  increases  of  course 
with  increasing  velocity.     On  the  other  hand,  equation  (6)  shows  that 
the  counter-flux  increases  also,  tending  toward  (f>0  as  a  limit.      Hence 
in  order  to  minimize  the  demagnetizing  action  for  a  given  amount  of 
power  to  be  absorbed,  it  is  best  to  use  a  large  magnetic  flux  and  a  low 
speed. 

(e)  Size  and  shape  of  pole-piece. — The  most  important  quantity  is  the 
width,  measured  in  a  direction  tangential  to  the  disk.     The  current  paths 
may  be  regarded  as  consisting  of  two  parts,  one  lying  in  a  radial  direction 
under  the  pole,  in  which  the  currents  are  induced,  and  the  other  consist- 
ing of  the  remainder  of  the  disk,  in  which  the  circuits  are  completed.     If 
the  polar  area  is  small  in  comparison  with  the  area  of  the  disk,  it  follows 
that  the  first  portion  mentioned  will  contain  most  of  the  ohmic  resistance 
of  the  circuits,  since  the  lines  of  flow  are  here  very  constricted.     Hence 
the  resistance  may  be  assumed  to  be  inversely  proportional  to  the  width 
of  pole.     If  now  the  same  total  flux  be  spread  out  over  a  pole-face  n  times 
as  wide,  the  total  current  will  remain  unchanged,  while  the  production  of 

heat  and  therefore  the  consumption  of  energy  will  be  -  as  great.    On 

the  other  hand,  if  the  magnetic  induction  remains  constant,  so  that  the 
total  flux  varies  directly  as  the  width  of  pole,  the  consumption  of  energy 
will  also  vary  in  the  same  manner. 

The  demagnetizing  effect  will  probably  be  somewhat  less  with  a  broad 
pole,  since  the  same  angular  lag  will  then  not  bring  the  demagnetizing 


44  A    BICYCLE    ERGOMETER   WITH   AN   ELECTRIC    BRAKE 

system  of  current  loops  so  directly  under  the  pole.  This  is  the  case  in 
the  damping  disk  of  watt-hour  meters,  which  in  addition  to  broad  pole- 
faces  employ  thin  disks  and  low  speeds,  thereby  reducing  the  demagnet- 
izing factor  to  a  minimum. 

Lengthening  the  pole-face  in  a  radial  direction  will,  by  reasoning 
analogous  to  the  preceding,  cause  a  proportionate  increase  in  the  ex- 
penditure of  energy  if  the  flux  density  is  kept  constant,  and  a  decrease 
in  the  same  ratio  if  the  total  flux  is  constant. 

(/)  Intensity  of  magnetic  field. — The  consumption  of  energy  varies 
as  the  square  of  the  flux  density.  The  percentage  of  demagnetization 
from  the  eddy  currents  is  a  constant  for  the  same  speed,  independent  of 
the  field  intensity.  This  explains  why  the  maxima  of  the  calibration 
curves  in  figs.  8  and  14  all  occur  at  practically  the  same  speed,  whatever 
the  current  in  the  electro-magnet. 

(gr)  Reluctance  of  the  magnetic  circuit. — To  insure  a  "stiff"  field,  re- 
sisting the  demagnetizing  action  of  the  eddy  currents,  it  would  be  advan- 
tageous to  use  a  magnetic  circuit  of  relatively  large  reluctance  and  large 
magnetomotive  force,  with  strongly  saturated  poles.  Crowding  of  the 
flux  in  the  neighborhood  of  the  trailing  edge  of  the  pole  could  be  reduced 
by  widening  the  air-gap  on  that  side  of  the  magnet,  or  by  using  split  pole- 
pieces,  like  those  in  the  Lundell  generators.  By  inserting  a  variable 
air-gap  in  the  magnetic  circuit,  the  maximum  of  the  calibration  curve 
could  probably  be  shifted  to  the  right  or  left. 

(h)  Location  of  magnet  poles. — These  should  be  far  enough  from  the 
outer  edge  of  the  disk  to  minimize  magnetic  leakage  around  the  edge. 
The  entire  magnet  should  be  shaped  in  such  a  way  as  to  reduce  the  leak- 
age, especially  in  the  neighborhood  of  the  poles.  This  requirement  is 
met,  for  example,  in  the  permanent  magnets  of  watt-hour  meters.  It  is 
true  that  our  calibration  curves  (fig.  13)  do  not  show  any  less  evidence  of 
demagnetization  when  the  poles  are  pushed  2  cm.  nearer  to  the  center  of 
the  disk,  but  this  is  because  there  was  still  considerable  opportunity  for 
magnetic  leakage,  owing  to  the  construction  of  the  magnet. 

Thus  on  the  whole  it  will  be  seen  that,  for  maximum  expenditure  of 
energy,  it  is  advantageous  to  use  small  magnet  poles,  while  to  minimize 
the  magnetic  reaction  the  poles  should  be  broad.  The  best  compro- 
mise between  these  opposing  factors  can  only  be  reached  by  experiment. 
In  any  case,  the  magnetic  field  should  be  as  intense  as  possible. 


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